Manel Achichi

Mohamed Ben Ellefi

Danai Symeonidou
email: danai.symeonidou@supagro.inra.fr

Konstantin Todorov
email: todorov@lirmm.fr

Automatic Key Selection for Data Linking

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In recent years, the Web of Data has been constantly growing both in terms of quantity of the RDF datasets published publicly on the web and in terms of diversity of the domains that they cover. One of the most important challenges in this setting is creating semantic links among these data [START_REF] Bizer | Linked data-the story so far[END_REF]. Among all possible semantic links that could be declared between resources found in different datasets, identity links, defined by the owl:sameAs statement, are of great importance and the ones that most of the attention is given to. Indeed, owl:sameAs links allow to see currently isolated datasets as one global dataset of connected resources. Considering the small number of existing owl:sameAs links on the Web today, this task remains a major challenge [START_REF] Bizer | Linked data-the story so far[END_REF].

Due to the large amount of data already available on the Web, defining manually owl:sameAs links would not be feasible. Therefore, many approaches try to answer to this challenge by providing different strategies to automate this process. Datasets conforming to different ontologies, data described using different vocabularies, datasets described in different languages are only several of the examples that make this problem hard to solve.

Many of the existing link discovery approaches are semi-automatic and require manual configuration. Some of these approaches use keys, declared by a domain expert, to link. A key represents a set of properties that uniquely identifies every instance of a given class. Keys can be used as logical rules to link data ensuring high precision results in the linking process. Additionally, they can be exploited to construct more complex rules. Nevertheless, keys are rarely known and are very hard to declare even for experts. Indeed, experts may not know all the specificities of a dataset leading to overlook certain keys or even introduce erroneous ones. For this reason, several automatic key discovery approaches have been already proposed in the context of the Semantic Web [START_REF] Symeonidou | SAKey: Scalable Almost Key discovery in RDF data[END_REF][START_REF] Atencia | Data interlinking through robust linkkey extraction[END_REF][START_REF] Soru | ROCKER: A refinement operator for key discovery[END_REF][START_REF] Pernelle | An automatic key discovery approach for data linking[END_REF][START_REF] Atencia | Keys and pseudo-keys detection for web datasets cleansing and interlinking[END_REF].

In spite of that fact, applying the output of these approaches directly is, in most of the cases, impossible due to the characteristics of the data. Ontology and data heterogeneity are not the only issues that can arise while trying to apply keys directly for data linking. Even if the datasets conform to the same ontology and the vocabulary of the properties is uniform, this does not ensure the success of the linking process. Very often, key discovery approaches discover a very large number of keys. The question that arises is whether all the keys are equally important among them, or there are some that are more significant than others. So far, no approach provides a strategy to rank the discovered keys, by taking in consideration their effectiveness for the matching task at hand.

Bridging the gap between key discovery and data linking approaches is critical in order to obtain successful data linking results. Therefore, in this paper we propose a new approach that, given two datasets to be linked, provides a set of ranked keys, valid for both of them. We introduce the notion of "effectiveness" of a discovered key. Intuitively, a key is considered as effective if it is able to provide many correct owl:sameAs links. In order to measure the effectiveness of keys, a support-based key quality criterion is provided. Unlike classic approaches using support for the discovered keys, in this work we introduce a new global support for keys valid for a set of (usually two) datasets.

The proposed approach can be summarized in the following main steps. (1) Preprocessing: in this step, given two datasets to be linked, only properties that are shared by both datasets are kept. This ensures that a key can be applied on both the source and the target datasets, and not only on each of them independently. At this point it is important to state that we consider that the datasets use either common vocabularies or that the explicit mapping between the respective vocabularies is known. (2) Merge: the key candidates discovered in each dataset are then merged by computing their cartesian product (recall that a key is a set of properties). (3) Ranking: we introduce a ranking criterion on the set of merged keys that is a function of the respective supports of each merged key in each dataset, normalized by the dataset sizes. (4) Keys combination: finally, the combined use of several top-ranked merged keys is evaluated, showing an improvement of the recall of a given link discovery tool.

The rest of the paper is structured as follows. Section 2 overviews data linking and automatic keys discovery and link specification approaches. Then, Section 3 presents our key ranking technique, evaluated in Section 4. Conclusions and future work are provided in Section 5.

Related Work

Let us look onto the process of data linking from a global perspective. The majority of the existing linking tools implement a process that consists of three steps: (1) configuration and pre-processing, (2) instance matching and (3) postprocessing.

Step (1) aims on the one hand to reduce the search space by identifying sets of linking candidates and key properties to compare, and on the other hand -to model instances by using a suitable representation that renders them comparable (one can think of indexing techniques, automatic translation, etc.).

Step (2) aims at deciding on a pair of instances whether they are equivalent or not, mostly relying on similarity of property values, evaluated by similarity measures defined in step [START_REF] Bizer | Linked data-the story so far[END_REF]. The output of step ( 2) is a set of matched instances, also known as a link set. Finally, step (3) allows to filter out erroneous matches or infer new ones, based on the link set provided in step [START_REF] Symeonidou | SAKey: Scalable Almost Key discovery in RDF data[END_REF].

The configuration step of the linking workflow described above contains two important sub-steps: (a) the choice of properties (or keys) across the two datasets whose values need to be compared, and (b) the choice of similarity measures to apply and their tuning. Our approach is tightly related to these sub-steps, although it does not fit into either of these categories. Indeed, we are not aware of the existence of other approaches that address the problem of key quality evaluation with respect to data linking, therefore, the current section looks into approaches relevant to both (a) and (b), as well as to the data linking process as a whole.

Automatic Linking Tools Configuration

Key Discovery. In order to link, many data linking approaches require a set of linking rules. Some data linking approaches use keys to build such rules. A key is a set of properties that uniquely identifies every resource of a given class. Nevertheless, keys are rarely known and also very hard to define even for expert.

In the context of Semantic Web, different key discovery approaches have been already proposed. Both [START_REF] Pernelle | An automatic key discovery approach for data linking[END_REF] and [START_REF] Symeonidou | SAKey: Scalable Almost Key discovery in RDF data[END_REF] propose a key discovery approach that follows the semantics of a key as defined by OWL. This definition states that two instances are referring to the same real world entity if at least one value per property appearing in a key is equal. Unlike [START_REF] Pernelle | An automatic key discovery approach for data linking[END_REF], [START_REF] Symeonidou | SAKey: Scalable Almost Key discovery in RDF data[END_REF] proposes a method that scales on large datasets, taking also into account errors or duplicates in the data. In [START_REF] Atencia | Keys and pseudo-keys detection for web datasets cleansing and interlinking[END_REF] and [START_REF] Soru | ROCKER: A refinement operator for key discovery[END_REF], the authors propose an alternative definition for the keys that is valid when the data are locally complete. In this case, to consider that two instances are equal, all the set of values per property appearing in a key should be the same. Finally, in [START_REF] Symeonidou | ICCS[END_REF], a key discovery approach for numerical data is proposed.

Atencia et al. [START_REF] Atencia | Data interlinking through robust linkkey extraction[END_REF] observe that key extraction is conducted by state-of-theart tools in an independent manner for two input datasets without taking into consideration the linking task ahead. The authors introduce the concept of a linkkey -a set of properties that are a key for two classes simultaneously, implying equivalence between resources that have identical values for the set of these properties.

Automatic Link Specification Algorithms. We consider the work on automatic link specification as related in terms of motivation to our approach and complementary in terms of application. Link specification is understood as the process of automatically building a set of linking rules (restrictions on the instances of the two datasets), choosing similarity measures to apply on corresponding property values across datasets together with their respective thresholds [START_REF] Ngomo | Eagle: Efficient active learning of link specifications using genetic programming[END_REF]. Several approaches have been introduced so far, mostly based on machine learning techniques, such as FEBRL [START_REF] Christen | Febrl-: an open source data cleaning, deduplication and record linkage system with a graphical user interface[END_REF], an extension of SILK [START_REF] Isele | Efficient multidimensional blocking for link discovery without losing recall[END_REF], RAVEN [START_REF] Ngomo | Raven-active learning of link specifications[END_REF] or, more recently, EAGLE [START_REF] Ngomo | Eagle: Efficient active learning of link specifications using genetic programming[END_REF]. Contrarily to key discovery methods, these approaches mainly focus on the automatic selection, combination and tuning of similarity measures to apply on the values of comparable properties. The identification of properties to compare is done by matching algorithms and no key computation is implied in this process. The efficiency of these algorithms can be improved if the system knows on which properties and on what types of values the similarity measures will be applied.

Data Linking

Data linking has evolved as a major research topic in the semantic web community over the past years, resulting in a number of approaches and tools addressing this problem. Here, instead of making an inventory of these techniques, surveyed in [START_REF] Ferrara | Data linking for the semantic web[END_REF] and [START_REF] Nentwig | A survey of current link discovery frameworks[END_REF], we scrutinize the main characteristics that unite or differentiate the most common approaches.

The majority of the off-the-shelf linking tools [START_REF] Jentzsch | Silk-generating rdf links while publishing or consuming linked data[END_REF][START_REF] Ngomo | LIMES -A time-efficient approach for large-scale link discovery on the web of data[END_REF][START_REF] Shao | Rimom-im: A novel iterative framework for instance matching[END_REF][START_REF] Jiménez-Ruiz | Logmap: Logic-based and scalable ontology matching[END_REF][START_REF] Nikolov | Integration of semantically annotated data by the knofuss architecture[END_REF][START_REF] Araujo | Serimi-resource description similarity, rdf instance matching and interlinking[END_REF] produce an RDF linkset of owl:sameAs statements relating equivalent resources and the linking process is commonly semi-automatic. As discussed above, the user has to configure manually a number of input parameters, such as the types of the instances to compare (with certain exceptions like [START_REF] Nikolov | Integration of semantically annotated data by the knofuss architecture[END_REF] where ontology matching techniques are applied to identify the equivalent classes automatically), the properties (or property chains) to follow, since most linking tools adopt a property-based link discovery philosophy, the similarity measure(s) and thresholds to apply on the literals and possibly an aggregation function for several measures. The bigger part of the existing approaches are conceived as general purpose linking methods and are designed to handle monolingual RDF data.

What differentiates these tools in the first place is the techniques of automatic preprocessing that are embedded in their architecture. Scalability and computational efficiency are major issues when dealing with data linking problems on the web scale. To reduce the search space, [START_REF] Araujo | Serimi-resource description similarity, rdf instance matching and interlinking[END_REF] cluster data items, based on their similarity with respect to their properties. Indexing techniques are used to reduce the number of instance comparisons by Rong et al. [START_REF] Rong | A machine learning approach for instance matching based on similarity metrics[END_REF] using similarity of vectors as a proxy for instance relatedness. Similarly, Shao et al. [START_REF] Shao | Rimom-im: A novel iterative framework for instance matching[END_REF] and Kejriwal et al. [START_REF] Kejriwal | Semi-supervised instance matching using boosted classifiers[END_REF] apply a blocking technique, which consists in using inverted indexing to generate candidate linking sets. SILK [START_REF] Jentzsch | Silk-generating rdf links while publishing or consuming linked data[END_REF] relies on indexing all target resources by the values of one or more properties used as a search term. LIMES [START_REF] Ngomo | LIMES -A time-efficient approach for large-scale link discovery on the web of data[END_REF] relies on the triangle inequality property of metric spaces to reduce the number of comparisons and thus the time complexity of the task.

The linking tools vary with respect to their abilities to handle different degrees and types of data heterogeneity. Indeed, most of the tools are able to cope with minor differences in spelling in the string literals by applying string matching techniques, but only a few are able to deal with more complex heterogeneities and just a couple of them try to resolve the problem of multilingualism (using different natural languages in data description), as Lesnikova et al. do, although in a very restricted scenario of only two languages [START_REF] Lesnikova | Interlinking english and chinese rdf data using babelnet[END_REF].

Positioning

The approach that is proposed in this paper attempts to close the gap between automatic key discovery algorithms and the data linking process. As observed above, the majority of key discovery techniques do not effectively facilitate the task of selection of properties whose values to compare in the linking process, due the large number of keys produced and the lack of confidence indicator coupled with the keys. Our method suggests to unlock the potential of key-based techniques by providing to the user of a data linking tool a limited number of quality keys, well-suited to the particular matching task. The only key-based approach that looks into the usefulness of keys for two datasets simultaneously, and not independently from one another, is [START_REF] Atencia | Data interlinking through robust linkkey extraction[END_REF]. In contrast to our approach, the set of linkkeys produced in [START_REF] Atencia | Data interlinking through robust linkkey extraction[END_REF] is unordered which does not allow to effectively select a key or decide on the use of one key as opposed to another.

As compared to automatic link specification algorithms cited in Subsection 2.1, our approach can be seen as complementary: we focus on the identification of a limited set of properties that can be used to effectively link datasets, while leaving the choice of the similarity measures, their combination and tuning to the user, or to the auto-configuring link specification methods given above. The automatic selection of keys can potentially improve the quality of link specification methods by restricting considerably the similarity space.

Automatic Key Ranking Approach

Given two RDF datasets, candidates to be linked, our approach aims at ranking the keys that are valid for both datasets. These keys can be used successfully as link specifications by link discovery frameworks. Before introducing the approach, recall the OWL definition of a key. A key is a set of properties, such that if two resources share at least one value for every property participating in this key, these resources are considered as equal, or formally: where X and Y are instances of the class c and p i (X, Z i ) ∧ p i (Y, Z i ) expresses that both X and Y share the same value Z i for every property p i in the key.

∀X, ∀Y, ∀Z 1 , . . . , Z n , ∧c(X) ∧ c(Y ) n i=1 (p i (X, Z i ) ∧ p i (Y, Z i )) ⇒ X = Y, (1)
In next section, we describe how do we select keys that are valid for the two datasets. Afterwards, we describe our ranking approach on the set of these keys.

Selecting Mutual Keys for Two Datasets and Merging

We start by giving one of our initial hypothesis. The number of available vocabularies has been growing with the growth of the LOD cloud, resulting in datasets described by a mixture of reused vocabulary terms. It is therefore often the case that two different datasets to be linked are described by different vocabularies. To answer to that, ontology alignment methods [START_REF] Shvaiko | Ontology matching: state of the art and future challenges[END_REF] are used in order to create mappings between vocabulary terms. In this paper, we assume that equivalence mappings between classes and properties across the two input datasets are declared (either manually, or by the help of an ontology matching tool). These mappings will be used to obtain keys that are valid for both datasets.

Algorithm 1 gives an overview of the main steps of our approach, also depicted in Figure 1. Overall, given two datasets to be linked, this algorithm returns a set of ranked keys valid for both datasets. In addition to that, every proposed key is given a score, allowing to rank keys according to their impact on the data linking process. This process is described step by step below.

First, given the datasets D S and D T containing instances of a class C, a set of property mappings M between the two datasets is computed. As described in [START_REF] Pernelle | An automatic key discovery approach for data linking[END_REF], property mappings allow the identification of properties that belong to both datasets simultaneously.

A key discovery step is applied to both datasets independently allowing the discovery of valid keys in each dataset. Only mapped properties, appearing in M , will be contained in the discovered keys. For this step, existing key discovery tools such as SAKey [START_REF] Symeonidou | SAKey: Scalable Almost Key discovery in RDF data[END_REF] or ROCKER [START_REF] Soru | ROCKER: A refinement operator for key discovery[END_REF] can be used to obtain keys for a given class C.

However, even if keys consist of properties that belong to both datasets, nothing ensures that the discovered keys found in each dataset independently will be the same. Indeed, there can be cases where something found as a key in one dataset it is not true in the other. Since key discovery approaches learn keys from the data, the generality of each dataset affects the generality of the discovered keys. For example, if a dataset contains people working in a specific university, it is possible to discover that the last name is a key. Thus, to deal with this challenge a merging step is performed. Indeed, merging keys coming from different datasets allows to verify the validity of discovered keys and to obtain more meaningful keys since they are applicable to more than one datasets. Different strategies for key merging could be applied. In this work, we apply a merging strategy proposed in [START_REF] Pernelle | An automatic key discovery approach for data linking[END_REF] providing minimal keys valid in both datasets.

The result is a set of merged keys considered as valid for both datasets. However, the number of merged keys produced by the algorithm can be significantly high, which makes manual selection difficult, particularly in the lack information of the keys suitability for the data linking task. Therefore, we introduce a novel ranking method for merged keys to identify the most suitable keys to be used in the link specification, introduced in next section.

Merged Keys Ranking

As described before, the merged keys are valid for both datasets. However, these keys may vary in terms of "effectiveness" in the linking process. Therefore, we propose to first to assign a score reflecting the "effectiveness" of a discovered key and second use this score to rank the discovered keys among them.

In general, it is very common that not all the properties are used to describe every instance of a given class. This happens often due to the nature of the property or the incompleteness of the data and may have significant impact on the quality of the discovered keys with respect to the linking task. While many properties apply to every instance of a class, there exist cases of properties that have values only for certain instances (the property "spouse" for a person applies only to people that are married). In addition, in the case when data are incomplete, an instance may not have a value for a specific property even if a value exists in reality. This can lead to the discovery of wrong keys since not all the possible scenarios are visible in the data. Since it is very hard to differentiate these two cases automatically and a manual identification would not be feasible due to the size of the existing datasets, we use the notion of support to measure the completeness of a key. The support measures the presence of a set of properties in a dataset. Intuitively, we tend to trust more keys that are valid for many instances in the data, i.e., keys with high support.

Basing ourselves on the support definition initially given by Atencia et al. in [START_REF] Atencia | Keys and pseudo-keys detection for web datasets cleansing and interlinking[END_REF], we redefine this measure in order to provide a ranking score for properties with respect to a given dataset.

Let D be an RDF dataset described by an ontology O. For a given class C ∈ O, let I C be the set of instances of type C and P the set of properties having an element of I C as a subject and let G C be the subgraph defined by the set of triples of I C and P , G C = {< i, p, . >: i ∈ I C , p ∈ P }.

Definition 1 (Property Support Score).

The support of a property p ∈ P with respect to the pair (D, C) is defined by:

supportP rop(p, D, C) = i∈I C < i, p, . > 1 |I C | .
In As keys for a given class can be composed of one or several properties, we introduce a ranking score for keys based on the supports of their properties, again with respect to their dataset.

Definition 2 (Key Support Score).

Let K = {p 1 , ..., p n } be a key corresponding to the pair (D, C), where p j ∈ P, j ∈ [1, n]. We define the support of K with respect to (D, C) as

supportKey(K, D, C) = i∈I C < i, K, . > 1 |I C | ,
where < i, K, . > means that ∀p j ∈ K, ∃ < i, p j , . >∈ G C .

In other words, supportKey(K, D, C) can be seen as a measure of the cooccurrence of {p 1 , ..., p n } in G C . To illustrate, let us consider a source dataset D S having 300 instances of type C S . Respectively, let D T be a target dataset having 100 instances of type C T , where C S and C T are two mapped (equivalent) classes, potentially sharing instances. Let K i and K j be two merged keys, obtained as described in Algorithm 1, with the following supports for (D S , C S ) and (D T , C T ), respectively:

supportKey(K i , D S , C S ) = 160 300 ; supportKey(K i , D T , C T ) = 40 100 ; supportKey(K j , D S , C S ) = 110 300 ; supportKey(K j , D T , C T ) = 90 100 .
Obviously, the challenge that arises here is how to rank the merged keys in order to ensure a maximum instance representativeness.

We note that key support score expresses the importance of a merged key with respect to each dataset, however, it is still necessary to provide a ranking function allowing to measure the importance of the merged keys for both datasets simultaneously.

An intuitive strategy to compute the final support of a merged key, given the supports computed locally in each dataset, would be to compute the average score of these supports. Nevertheless, this strategy would fail to capture all the different scenarios that could lead to a support value. For example, a key having supports 1 and 0.4 in datasets 1 and 2, would have the same merged support than a key having supports of 0.7 and 0.7 in datasets 1 and 2 respectively. Thus, we propose a multiplication function between already computed key supports which ensures better results in the context of data linking evaluation. Consequently, we adopt this ranking function as defined below.

Definition 3 (Merged Keys Rank Function). We define the rank of a merged key K with respect to two datasets D S and D T and two classes C S and C T as:

mergedKeysRank(K) = supportKey(K, D S , C S ) × supportKey(K, D T , C T ).
Applying the ranking to our example, we obtain the following scores: globalRank(K j ) = 0.33; globalRank(K k ) = 0.22; globalRank(K i ) = 0.21; Therefore, in this example, the key K j is more important than K i which means that intuitively should lead to better data linking results.

Evaluation

In order to confirm the effectiveness of the proposed approach, we have conducted an experimental evaluation applying two state-of-the-art key discovery tools: SAKey and ROCKER. We have used two different datasets, a real-world dataset coming from the DOREMUS project1 and a synthetic benchmark provided by the Instance Matching Track of the Ontology Alignment Evaluation Initiative (OAEI) 20102 . The current experiments were applied on links generated semi-automatically using the linking tool SILK. In this evaluation, we highlight a set of issues raised during these experiments. But first, let us define the criteria and the measures used for this evaluation. Two aspects are taken into account through the keys ranking performed using our approach, first the correctness that determines whether the discovered links are correct and second, the completeness that determines whether all the correct links are discovered. These criteria are evaluated by the help of three commonly used evaluation metrics:

-Precision: expresses the ratio between the cardinalities of the set of valid matchings and all matching pairs identified by the system. -Recall : expresses the ratio between the cardinalities of the set of valid matchings and the all matching pairs that belong in the reference alignment. -F-Measure: is computed by the following formula :

F-Measure = 2 * P recision * Recall P recision + Recall
We note that all considered pairs of datasets are using the same ontology model, hence, the ontology mapping process is not considered in our experiments. We first execute SAKey or ROCKER on each dataset in order to identify the set of keys. However, we emphasize the fact that advanced key exceptions like pseudo-keys or almost keys are not the focus of this paper, therefore, only traditional keys are discovered. These keys are then merged and ranked according to their support score. We launch SILK iteratively as many times as the number of the retrieved keys and produce an F-measure at each run by the help of the reference alignment of our benchmark data. We expect to find a monotonic relation between the ranks of keys and the F-measure values produced by SILK by using these keys. Note that the purpose of these experiments is not to evaluate the performance of the linking tools, but to evaluate the quality of the automatically computed ranks of keys. In other words, we assess whether the generated links are increasingly correct in an ascending order of the ranked keys.

Experiments on the DOREMUS Benchmark

The data in our first experiment come from the DOREMUS project and consists of bibliographical records found in the music catalogs of two major French institutions -La Bibliothque Nationale de France (BnF) and La Philharmonie de Paris (PP). These data describe music works and contain properties such as work titles ("Moonlight Sonata"), composer (Beethoven), genre (sonata), opus number, etc.. The benchmark datasets were built based on these data with the help of music librarian experts of both institutions, providing at each time sets of works that exist in both of their catalogs, together with a reference alignment. The data were converted from their original MARC format to RDF using the marc2rdf prototype3 [START_REF] Achichi | Doremus: Doing reusable musical data[END_REF]. We consider two benchmark datasets 4 , each manifesting a number data heterogeneities:

1) DS1 is a small benchmark dataset, consisting of a source and a target dataset form the BnF and the PP, respectively, each containing 17 music works. These data show recurrent heterogeneity problems such as letters and numbers in the property values, orthographic differences, missing catalog numbers and/or opus numbers, multilingualism in titles, presence of diacritical characters, different value distances, different properties describing the same information, missing properties (lack of description) and missing titles. SAKey produced eight keys in this scenario. The three top-ranked merged keys using our approach are:

1. K1: {P 3 has note} 2. K2: {P 102 has title} 3. K3: {P 131 is identif ied by, P 3 has note}, where P 3 has note, P 102 has title, P 131 is identif ied by and P 3 has note correspond to a comment, title, composer and creation date of a musical work, respectively.

As we can see in Figure 2(a), our ranking function ensures a decrease of the F-measure with the decrease of the key-rank, in the prominent exception of the top-ranked key, which obtains a very low value of F-Measure. This is explained by the nature of the property P 3 has note. This property describes a comment in a free format text written by a cataloguer providing information on the works, creations or authors of such works. The values for this property for the same work are highly heterogeneous (most commonly they are completely different) across the two institutions, which introduces noise and considerably increases the alignment complexity between these resources. Thus, we decided to conduct a second experiment on the same data by removing the property has note in order to confirm our observation. Figure 2 (b) reports the results of this experiment and shows a net decrease of the curve. Overall, the experiment showed that our ranking approach is efficient and the misplaced key is due to the heterogeneous nature of data.

The same experiment has been conducted using this time the key discovery approach ROCKER. The results are reported in Figure 3 showing that the keys were well ranked. Note that, due to the different keys identification definition used by ROCKER, the problematic property has note did not appear in the keys produced by the system. Fig. 3: Results on DS1 by using ROCKER.

2) DS2 is a benchmark dataset consisting of a source and a target dataset from the BnF and the PP, respectively, each composed of 32 music works. Contrarily to DS2, these datasets consist of blocks that are highly similar in their description works (i.e., works of the same composer and with same titles).

The results on this dataset by using SAKey are reported in Figure 4(a). The three top-ranked merged keys are:

1. K1: {P 3 has note, P 102 has title, P 131 is identif ied by} The results of this experiment are similar to the first one. Not considering the property P 3 has note improves considerably (see Figure 4

Experiments on the OAEI Benchmark Data

In the second series of experiments, we apply our ranking approach on keys identified in datasets proposed in the instance matching track of OAEI 2010. In this work, we report the obtained results on the dataset P erson1. The results by using SAKey and ROCKER are shown in Figure 5(a) and (b), respectivey, where one can notice that there is an overall decrease in the F-Measure values in the two cases. Note that in Figure 5(a), there are some problematic key-ranks, showing increase in F-measure while the ranks descend. We observed that SILK achieves better results comparing string characters than numeric characters. Indeed, this explains why we have had an increasing curve between the keys K7 and K8, knowing that they are composed of street and house number properties (street and surname properties), respectively.

Top Ranked Keys Complementarity

In this evaluation, we want to examine whether using the k (we have taken k = 3) top-ranked keys in combination can improve the linking scores as compared to using only one of the top-ranked keys (e.g., the first one) for linking. As discussed above, even if a key is discovered as a first-rank key, nothing ensures that the vocabulary used in both datasets to describe that key is homogeneous. To answer to that, combining a set of top ranked keys would lead to better linking results. Notice that by doing so, the recall value remains the same or increases as compared to the single key approach, while the precision may increase (if the proportion of the positive matching pairs becomes larger than the negative matching pairs) as it may as well decrease. As shown in Table 1, the experiments on DOREMUS datasets using the three top ranked keys increased relatively (in bold in the table) the F-Measure with respect to the first-rank key (where the improved values are in italics) and significantly the recall scores (more positive matching pairs were recovered). Thus, it seems reasonable to conclude that merging the matching results retrieved from the top ranked keys allows to improve significantly the results in terms of recall, while this cannot guarantee an improvement in precision.

Conclusion and Future Work

This paper presents an approach that allows to select automatically a number of merged keys, relevant for a given pair of input datasets, and rank them with respect to their "effectiveness" for the task of discovering owl:sameAs links between them. The effectiveness of a merged key is defined as a function of the combination of its respective supports on each of the two input datasets. The proposed method allows to reduce significantly the user effort in the selection of keys used as a parameter of a data linking tool, such as SILK or LIMES. In this way, we attempt to bridge the gap between configuration-oriented approaches, such as automatic key discovery and automatic link specification, and the actual process of data linking. We also look into the complementarity properties of a small set of top-ranked keys and show that their combined use improves significantly the recall. To demonstrate our concepts, we have conducted a series of experiments on data coming from the OAEI campaign, as well as on real-world data from the field of classical music cataloguing.

In near future, we plan to improve our ranking criterion by defining it as a function of the estimated intersection of the sets of instances covered by a given key across two datasets.

Fig. 1 :

 1 Fig. 1: The processing pipeline of Alg. 1.

Algorithm 1 :

 1 The merged keys ranking algorithm. Input: D S and D T , a pair of datasets candidates to be linked. Output: A set of merged and ranked keys: rankedMergedKeys 1 M ← Mapping(D S , D T ); 2 KeysD S ← keysDiscovery(D S , M ); 3 KeysD T ← keysDiscovery(D T , M ); 4 MergedKeys ← keysMerging(KeysD S , KeysD T ); 5 rankedMergedKeys ← mergedKeysRanking(D S , D T , MergedKeys); 6 return rankedMergedKeys;

  other words, supportP rop(p, D, C) = N 1 |I C | means that N instances of type C in the dataset D have a value for the property p (supportP rop(p, D, C) ∈ [0, 1]).

Fig. 2 :

 2 Fig. 2: Results by using SAKey on DS1: (a) by considering all properties, (b) without the property has note.to conduct a second experiment on the same data by removing the property has note in order to confirm our observation. Figure2(b) reports the results of this experiment and shows a net decrease of the curve. Overall, the experiment showed that our ranking approach is efficient and the misplaced key is due to the heterogeneous nature of data.The same experiment has been conducted using this time the key discovery approach ROCKER. The results are reported in Figure3showing that the keys were well ranked. Note that, due to the different keys identification definition used by ROCKER, the problematic property has note did not appear in the keys produced by the system.

2 .Fig. 4 :

 24 Fig. 4: Results by using SAKey on DS2: (a) by considering all properties, (b) without the property has note.

  (a) and (b)) the keys ranking. Indeed, as shown in Figure 4 (a), the key K5 which is composed by the properties P 102 has title, U 35 had f unction of type and P 3 has note has significantly lowered the f-measure value; which is not the case of the keys in Figure 4 (b).

Fig. 5 :

 5 Fig. 5: Results on the dataset Person1: (a) by using SAKey, (b) by using ROCKER.The three top ranked merged keys (in Figure5(a)) on the dataset Person1 using SAKey are:1. K1: {soc sec id}, 2. K2: {given name, postcode} 3. K3: {surname, postcode}, where the properties soc sec id, given name, surname and postcode correspond to the social security number, given name, surname and postal code address of a person, respectively. In the same manner, we reiterated the experiment using ROCKER which gives better results as shown in Figure5(b).

Table 1 :

 1 Results of the combination of the three top-ranked keys on the DORE-MUS datasets.

				SAKey					ROCKER
		Dataset 1	Dataset 2	Dataset 1	Dataset 2
		F	P	R	F	P	R	F	P	R
	K1 K2 K3	0.12 0.12 0.11 0.5 0.75 0.37 0.59 0.8 0.47 0.71 0.9 0.58 0.48 0.7 0.37 0.2 0.66 0.11 0.52 1 0.35 0.37 0.56 0.28 0.2 0.66 0.11	No merged key has been identified.
	K1+K2+K3 0.54 0.44 0.7 0.51 0.63 0.43 0.62 0.75 0.52

http://www.doremus.org

http://oaei.ontologymatching.org/2010/

https://github.com/DOREMUS-ANR/marc2rdf

Doremus datasets, together with their reference alignments, are available at http: //lirmm.fr/benellefi/doremus-bench

Acknowledgements

This work has been partially supported by the French National Research Agency(ANR) within the DOREMUS Project, under grant number ANR-14-CE24-0020.


Hajj Ali Hassan

Michaux Florentin
email: florentin.michaux@univ-lorraine.fr.

Bouelet Ntsama

Isabelle Sandrine

Durand Pierrick

Jasniewski Jordane

Michel Linder

Florentin Michaux

Libio

Shea butter solid nanoparticles for curcumin encapsulation: influence of nanoparticles size on drug loading †

Keywords: solid lipid nanoparticles, SLN, shea butter, curcumin, colloidal carrier, lipid polymorphism SLN, Solid Lipid Nanoparticles, EE, Encapsulation Efficiency, XRD, X-Ray Diffraction, SAXS, Small Angle X-ray Scattering, WAXS, Wide Angle X-Ray Scattering, DSC, Differential Scanning Calorimetry, DLS, Dynamic Light Scattering, PdI, Polydispersity Index, MDOE, Mixture Design Of Experiments, RSM, Response Surface Methodology

In the present work, shea butter solid lipid nanoparticles (SLN) were prepared by sonication using nonionic surfactants as stabilizers without organic solvent. The mixture design methodology enabled to control particles size from 50 nm to more than 1 µm according to the mixture composition. Then, curcumin, a natural polyphenol, has been encapsulated in nanoparticles with a wide range of diameters (50-230 nm) and the encapsulation efficiency has been related to the particles sizes. The bigger the nanoparticles, the lower the encapsulation efficiency. The lipid structure at non dispersed state and under SLN form has been studied by Differential Scanning Calorimetry (DSC) and X-ray diffraction (XRD). From the obtained results, it seemed that encapsulated curcumin did not affect the lipid properties at the SLN state unlike at non dispersed state. This was consistent with a localization of the curcumin in the outer shell of the lipid nanoparticles which explained the evolution of the encapsulation efficiency according to the nanoparticles size.

Practical applications

Solid lipid nanoparticles (SLN) present a great interest in the delivery of both hydrophobic and hydrophilic drugs. Preparing such nanovectors with natural, non-expensive materials and easily available (i.e. shea butter) will promote their potential use in several applications like oral, parenteral, dermal or ocular delivery. Controlling the particles size from the formulation composition and also the drug loading from SLN properties is of main importance to optimize the use of SLN as colloidal carrier.

Introduction

Solid lipid nanoparticles (SLN), developed since the beginning of the 90's [START_REF] Siekmann | Submicron-sized parenteral carrier systems based on solid lipids[END_REF][START_REF] Muller | Solid Lipid Nanoparticles (Sln) -an Alternative Colloidal Carrier System for Controlled Drug-Delivery[END_REF], are an alternative carrier to liposomes, emulsions and polymeric particles promising for various applications as oral [START_REF] Das | Recent Advances in Lipid Nanoparticles Formulations with Solid Matrix for Oral Drug Delivery[END_REF], dermal [START_REF] Mehnert | Solid lipid nanoparticles. Production, characterization and applications[END_REF][START_REF] Pardeike | Lipid Nanoparticles (SLN, NLC) in cosmetic and pharmaceutical dermal products[END_REF], parental [START_REF] Mehnert | Solid lipid nanoparticles. Production, characterization and applications[END_REF] delivery of either hydrophobic or hydrophilic actives. SLN are produced by cooling a nanoemulsion prepared at a temperature higher than the melting point of the composing lipid and thus are solid at room temperature. This property induces a better physical stability compared than liquid/liquid systems as emulsions or liposomes [START_REF] Müller | Solid lipid nanoparticles (SLN) for controlled drug deliverya review of the state of the art[END_REF]. A wide range of lipid has been investigated for SLN preparation [START_REF] Das | Recent Advances in Lipid Nanoparticles Formulations with Solid Matrix for Oral Drug Delivery[END_REF][START_REF] Mehnert | Solid lipid nanoparticles. Production, characterization and applications[END_REF]. Shea butter is an extensively used fat in West Africa and is employed in food, cosmetic and pharmaceutical industries. Shea butter is a good candidate for SLN production, taking into account its simple fatty acids composition (mainly stearic and oleic acids) [START_REF] Honfo | Nutritional Composition of Shea Products and Chemical Properties of Shea Butter: A Review[END_REF] leading to a unique low melting temperature (ranging from 33 to 38 °C), its natural origin and its low price. In addition to the triacylglycerols, the presence of tocopherol and other phenolic compounds in Shea butter is moreover of special interest due to their antioxidant and anti-inflammatory properties highlighted in food and cosmetic uses [START_REF] Honfo | Nutritional Composition of Shea Products and Chemical Properties of Shea Butter: A Review[END_REF].

Nevertheless, to the best of our knowledge, only one recent study reports the use of shea butter for the preparation of solid lipid nanoparticles [START_REF] Raffin | Natural Lipid Nanoparticles Containing Nimesulide: Synthesis, Characterization and In Vivo Antiedematogenic and Antiedematogenic and Antinociceptive Activities[END_REF].

Lipid nanoparticles have been already used to incorporate many actives compounds reported in several reviews [START_REF] Pardeike | Lipid Nanoparticles (SLN, NLC) in cosmetic and pharmaceutical dermal products[END_REF][START_REF] Müller | Solid lipid nanoparticles (SLN) for controlled drug deliverya review of the state of the art[END_REF][START_REF] Muller | Solid lipid nanoparticles (SLN) and nanostructured lipid carriers (NLC) in cosmetic and dermatological preparations[END_REF][START_REF] Li | Preparation and Stability of Astaxanthin Solid Lipid Nanoparticles Based on Stearic Acid[END_REF]. Some recent studies deal with the encapsulation of polyphenols such as quercetin or curcumin into SLN [START_REF] Wang | Anti-inflammatory activity of curcumin-loaded solid lipid nanoparticles in IL-1β transgenic mice subjected to the lipopolysaccharide-induced sepsis[END_REF][START_REF] Noack | Physicochemical characterization of curcuminoid-loaded solid lipid nanoparticles[END_REF][START_REF] Li | Enhancement of gastrointestinal absorption of quercetin by solid lipid nanoparticles[END_REF]. Curcumin is a natural hydrophobic polyphenol extracted from the roots of Curcuma longa and present in turmeric used as food additive. Several studies report the antioxidant, anti-inflammatory, antibacterial and also anti-cancer properties of curcumin [START_REF] Noack | Physicochemical characterization of curcuminoid-loaded solid lipid nanoparticles[END_REF][START_REF] Duvoix | Chemopreventive and therapeutic effects of curcumin[END_REF]. Its main drawback for an oral delivery is its low solubility in water and so, its poor bioavailability. To overcome this problem, several research teams focus their works on encapsulation of curcumin in nanovectors such as nanoliposomes, nanoemulsions, and solid lipid nanoparticles [START_REF] Noack | Physicochemical characterization of curcuminoid-loaded solid lipid nanoparticles[END_REF][START_REF] Liu | Recent Progress in Studying Curcumin and its Nanopreparations for Cancer Therapy[END_REF][START_REF] Ahmed | Nanoemulsionand emulsion-based delivery systems for curcumin: Encapsulation and release properties[END_REF]. Curcumin is also often used as a lipophilic model compound for the development of drug carriers [START_REF] Ahmed | Nanoemulsionand emulsion-based delivery systems for curcumin: Encapsulation and release properties[END_REF] thanks to its facility to be detected by its intensive yellow color (curcumin is also used as a food colorant) and a specific absorption at 425 nm.

Three models describing the distribution of the active molecule inside the nanoparticles are reported in the literature, i) homogeneous matrix model, ii) core-shell model, drug-enriched shell and iii) core-shell model, drug-enriched core [START_REF] Müller | Solid lipid nanoparticles (SLN) for controlled drug deliverya review of the state of the art[END_REF][START_REF] Muller | Solid lipid nanoparticles (SLN) and nanostructured lipid carriers (NLC) in cosmetic and dermatological preparations[END_REF]. Obviously, the encapsulation efficiency (EE) and the drug release depend on its distribution in the particle [START_REF] Joshi | Lipid nanoparticles for parenteral delivery of actives[END_REF]. Controlling the nanoparticles properties should allow a better control of the drug encapsulation specificities. Mixture design methodology is a powerful technique to assess the nanoparticles properties according to the system composition. Indeed, it allows the determination of the influence of the system properties on several physico-chemical parameters using a minimum number of experiments. This methodology has been already used to study the effect of several parameters onto the properties of SLN prepared by emulsification-solvent evaporation or solvent diffusion methods [START_REF] Zhang | Experimental design for the optimization of lipid nanoparticles[END_REF][START_REF] Vitorino | The size of solid lipid nanoparticles: An interpretation from experimental design[END_REF].

Solvent: lipid ratio, lipid concentration and temperature seem to be the key parameters to control the particles size.

In the present work, mixture design methodology has been used to control shea butter nanoparticles size prepared without organic solvent as a function of the ternary system composition (lipid, water, and nonionic surfactant fractions). Curcumin has been incorporated in different particles of different sizes to evidence the influence of the nanoparticles diameter on EE.

The aim of this study was to obtain nanoparticles of different sizes from identical lipid contents to determine how the curcumin loading is influenced by the SLN size. Moreover, the effect of the encapsulated molecule on the structure of the lipid matrix is discussed from DSC and XRD experiments at low and wide angles and shed some light on its localization inside the nanoparticle.

Materials and methods

Materials

Shea butter was purchased from IeS Labo (Oraison, France). Main fatty acids were stearic (42.3 wt.%) and oleic (43.9 wt.%) acids confirmed by gas chromatography experiments (data not shown). Its melting point was determined from DSC measurements at 37 °C. Tween 80, Span 80 and curcumin were purchased from Sigma-Aldrich.

Methods

2.a. Shea butter nanoparticles preparation

The ternary system was composed of shea butter as lipophilic phase, a mixture of Tween 80 (hydrophilic surfactant) and Span 80 (lipophilic surfactant) (mass ratio 90/10) as emulsifiers and ultrapure water in several proportions (Table 1). First, the lipid was melted at 40 °C and mixed with Span 80. Tween 80 was solubilized in ultrapure water at the same temperature under stirring (500 rpm) until the solution became transparent (micellar solution). The lipid phase containing Span 80 was then added dropwise to the micellar solution of Tween 80 at 40 °C under stirring at 500 rpm. The obtained pre-emulsion was homogenized using Ultra-Turrax system (IKA T25) during 5 min at 10,000 rpm and then sonicated in pulse mode (1s on, 1s off) using Vibracell 75115 from Bioblock Scientific at 40% of the maximal power during 6 min. The sample temperature was maintained at 40 °C all along the procedure. The obtained nanoemulsion was then cooled down slowly at 20 °C for the crystallization process and stored at 4 °C.

2.b. Mixture design methodology

Mixture Design Of Experiments (MDOE) is a methodology used to determine the optimum combination of constituents by using response surface methodology (RSM). Scheffé simplex centroid design was used with a three-component mixture, with lower and upper limit restrictions and test points. The studied variables were: shea butter (from 5 to 40 wt.%), water (from 48 to 92 t.%) and surfactant (from 1.5 to 19 wt.%). The nanoparticle hydrodynamic diameters and the polydispersity index of the dispersion were optimized using the NEMROD software (New Efficient Methodology for Research using Optimal Design). [START_REF] Mazerolles | Computer-Assisted Optimization with Nemrod Software[END_REF] The ternary mixture component ratios are given in Table 1. Data from the nanoparticles characterizations were used to calculate the special cubic equation for three components (Equation 1):

y = β 1 x 1 + β 2 x 2 + β 3 x 3 + β 12 x 1 x 2 + β 13 x 1 x 3 + β 23 x 2 x 3 + β 123 x 1 x 2 x 3 (Eq 1)
where y was the studied response (nanoparticle hydrodynamic diameters and polydispersity index), β ijk were regression parameters and x 1 , x 2 and x 3 represented the levels of three constituents. The validity of the model was tested by addition of further test points, which were incorporated into the design for analysis. The coefficients of the reduced cubic model were fitted to the data by least squares multi-linear regression and the goodness of fit was investigated by analysis of variance (ANOVA).

In the mixture design, the effect of the change of variables on the responses can be observed on the ternary contour map.

2.c. Curcumin solubility in shea butter

The EE was related to the maximal solubility of curcumin in the lipid phase. This solubility was determined as follow. Aliquot of 5 mg of curcumin was added to the 5 mL of melted lipid at 40 °C and kept under stirring for 3 days protected from light [START_REF] Hasan | Liposome encapsulation of curcumin: Physico-chemical characterizations and effects on MCF7 cancer cell proliferation[END_REF]. The blend then was centrifuged 15 min at 12100 x g at 40 °C. The non-dissolved (crystalline) curcumin was removed and the supernatant was diluted with methanol for absorbance measurements at 425 nm (UV-Vis 1605 spectrophotometer, Shimadzu, Japan). In parallel, a calibration curve was realized from different solutions of curcumin in methanol. The amount of curcumin solubilized in shea butter was calculated from the calibration curve equation. A sample without curcumin is used as blank to perform measurements. Experiments were done in triplicate.

2.d. Curcumin encapsulation into shea butter nanoparticles

Concerning the curcumin encapsulation, the procedure was similar to the nanoparticles preparation one despite the fact that the curcumin was added to the lipid phase (shea butter + Span 80). The curcumin quantity was calculated from its maximal solubility in the lipid phase and the mass of shea butter used for the formulation. The weight of curcumin could vary according to the system composition and was related to the shea butter content. The EE of the curcumin (see below) was calculated from its solubility in the lipid phase. Therefore, the results obtained with different compositions could be compared. After the preparation (homogenization by Ultra-Turrax and sonication), cooled samples (left enough time, more than one night, at room temperature to allow lipid crystallization confirmed by XRD experiments) were centrifuged at 3000 x g at room temperature during 5 min to precipitate free curcumin. The supernatant was then centrifuged in Centrisart ultrafilters (100 kDa molecular weight cut of, Sartorius) to remove remaining micelles which can incorporate a little amount of curcumin at 1400 x g during 20 min. The recovered SLN dispersion was diluted in methanol for absorbance analysis according to the calibration curve. The amount of encapsulated curcumin was calculated from the calibration curve (see section 2.c).

The curcumin amount used for encapsulation experiments was calculated from the weight of shea butter used and its solubility in the lipid phase. It corresponded to the maximal quantity of curcumin which could be dissolved in the lipid. Then, the EE was determined with the Equation 2.

(Eq.2)

Therefore, an EE of 100% meant that the curcumin maximal solubility in the lipid was reached in the nanoparticles and that all the molecules remained in the particles after lipid solidification.

Even, if both compositions and curcumin weight were different, it was possible to compare the obtained EE as a function of the nanoparticles size.

2.e. Nanoparticles size analysis

The first part of the study consisted to control the size distribution of the lipid nanoparticles as a function of the system composition. The mean diameter (d.nm) and the polydispersity index (PdI)

were measured at 20 °C by Dynamic Light Scattering using a Zetasizer Nano ZS (green laser at 532 nm) from Malvern Instruments analyzed by the CONTIN algorithm. Samples were diluted 100 times before the analysis to avoid detector saturation. The presented nanoparticles diameters came from the intensity weighing distribution which was the most accurate to describe the system. The presence of residual micelles in the SLN dispersion could indeed lower the z-average value obtained from DLS measurements which was then not representative of the SLN size.

Measures were performed in triplicate.

2.f. Differential Scanning Calorimetry (DSC)

Calorimetric measurements were performed using a DSC1 differential scanning calorimeter equipped with a high sensitivity HSS8 probe from Mettler-Toledo. (Low temperature studies were achieved using a liquid nitrogen cooling system that allows reaching 123 K in the sample holder.) About 10 mg of powder was accurately weighted for each sample and sealed in aluminum pans with a mechanical crimp and at a constant scan rate of 5 K.min -1 . The temperature and energy were calibrating using indium, zinc, and mercury as references.

2.g. X-Ray diffraction analysis (XRD)

The XRD measurements were performed using a Panalytical X'Pert Pro diffractometer equipped with a Cu tube, a Ge (111) incident-beam monochromator (α = 1.5406 Å) and an X'Celerator detector. WAXS measurements were collected using 0.02 rad Soller slits, programmable divergence and anti-scatter slits, the irradiated area was fixed to 10mm  10mm. The X'Celerator detector was used as "scanning line detector (1D)" with 2.122° active length. Data collection was carried out in the scattering angle range 2-30° with a 0.0167° step over 90 min. SAXS measurements were collected using 0.02 rad Soller slits, 1/16° fixed divergence and anti-scatter slits. The X'Celerator detector was used as "scanning line detector (1D)" with 0.518° active length.

Data collection was carried out in the scattering angle range 0.8°-12° with a 0.0167° step over 90 min. Since the diffractometer is based on Bragg-Brentano θ-2θ geometry, the sample holder moves around θ causing any liquid sample to slip off the sample holder. As a consequence the 8 liquid SLN samples were filled into the X-ray holder, and covered with a thin aluminium foil. The aluminium foils presents diffraction peaks at higher angles, and causes a small absorption of the X-Ray intensity.

Results and discussion

Influence of the ternary system composition on shea butter nanoparticles size distribution from mixture design methodology

The mixture design methodology was applied to study the influence of the formulation composition on the shea butter nanoparticles diameter and polydispersity. The experimental area was limited to a domain defined by: 5-40 wt.% of shea butter ; 48-92 wt.% of water and 1. point of view, the size evolution upon the system composition was consistent with the expected results since smaller particles were obtained for low shea butter content and high surfactant concentrations and vice versa. Increasing the shea butter proportion or lowering the surfactant amount led to an increase of the SLN diameter. According to these results, the nanoparticle size was controlled by the amount of surfactant which could stabilize the interface between the water and the lipid phases. Higher the surfactant concentration, greater the interface, and so smaller the particles for a given lipid fraction. Likewise, for an identical surfactant content, the increase of the shea butter fraction led to bigger particles. Knowing the surface per polar head of the surfactant (60 Å 2 for Tween 80 from surface tension measurements) allowed to estimating the nanoparticle size as a function of the lipid and surfactant contents from a simple calculation. The polydispersity index (PdI) varied from 0.12 to 0.80 (Table 1). Nanoparticles dispersions were considered as monodispersed since PdI is lower than 0.2. The less polydispersed systems were recovered in the center of the studied domain (Fig. 1.C.).

The mixture design methodology allowed modeling the influence of the formulation composition on the studied responses (size and PdI). Then, it was possible to predict the SLN sizes as a function of the composition in the identical experimental range. The model depended on coefficients related to the fraction of each constituent and also from the interactions between them. The mixture design of experiments led to the following equations: This model enabled an easy preparation of shea butter nanoparticles of different diameters in order to study the influence of the SLN size on the curcumin encapsulation efficiency.

Size (nm) = -

Curcumin solubility in shea butter

In order to calculate the curcumin EE in shea butter nanoparticles, it was necessary in a first step to determine its solubility in the lipid which corresponded to the maximum amount that could be incorporated in the nanoparticles. From absorbance measurements, the curcumin solubility in the lipid matrix at 40 °C (liquid lipid) was determined to 0.33 mg.g -1 of shea butter (0.33 wt.%). The curcumin solubility was related to the averaged molecular weight of the lipid [START_REF] Ahmed | Nanoemulsionand emulsion-based delivery systems for curcumin: Encapsulation and release properties[END_REF]. Short chain triglycerides favored curcumin solubility thanks to interactions between polar groups of both components, since short chain compounds had more polar groups per unit mass than long chain triglycerides. The value determined in this study was close to the one reported for corn oil (long chain triglycerides) of 0.30 mg.g -1 of lipid by Ahmed et al. [START_REF] Ahmed | Nanoemulsionand emulsion-based delivery systems for curcumin: Encapsulation and release properties[END_REF] Curcumin solubility was determined at 40 °C to evaluate the amount of curcumin remaining into the SLN after the lipid crystallization step.

Curcumin Encapsulation in SLN

From the mixture design experiments, several compositions leading to different nanoparticles sizes from 50 to 200 nm were chosen in order to evidence the effect of the nanoparticles diameter on the curcumin encapsulation efficiency. The EE was measured after the solidification of lipids. It then corresponded to the curcumin amount which remained in the lipid phase after emulsification and crystallization (see section 2.d). The biggest size was limited to 200 nm to focus the study on narrow particles population. Indeed, from the first set of experiments, the PdI increased upon the particles sizes (Table 1). The polyphenol mass added to the system was calculated from its 10 solubility in the lipid at 40 °C and from the mass of shea butter used. This way enabled to compare the influence of the nanoparticle size on the drug loading independently from the lipid concentration. The results obtained from these additional experiments are summarized in Table 2.

Firstly, the measured SLN diameters were closed to the predicted ones (errors around 15%) except for one experiment. These additional preparations confirmed the numerical model coming from the mixture design part. Concerning the PdI, some differences between predicted and measured values were also important for several experiments but the PdI values remain lower or close to 0.2. Moreover, the SLN preparations were performed with and without curcumin. No significant differences were reported in terms of size and polydispersity for particles with and without the polyphenol. The presence of curcumin in the lipid did not modify the SLN size distribution whatever the nanoparticles diameter. The second and main result reported in Table 2 The evolution of EE appeared to be linear upon SLN size (line on Fig. 2.A) in the studied nanoparticle diameters range according to the following equation: EE (%) = -0.3743*nanoparticles diameter + 106 R 2 = 0.93 (Eq.5)

It was then possible to deduce the EE directly from the system composition according to Eq.3 (size upon formulation composition) and Eq.5.

Three models are reported in the literature concerning the localization of a guest molecule in solid lipid nanoparticles, i) homogeneous matrix, ii) shell-enriched and iii) core-enriched [START_REF] Muller | Solid lipid nanoparticles (SLN) and nanostructured lipid carriers (NLC) in cosmetic and dermatological preparations[END_REF]. Depending on these models, the evolution of the encapsulation efficiency upon the nanoparticles diameter may vary differently. If the guest molecule is homogeneously distributed in the lipid matrix, the EE should not depend on the size of the nanoparticles. If the active compound is localized in a lipid shell around a pure lipid core, smaller the particles are, higher the EE should be since the surface of the particles increases when the diameter decreases for a constant mass. On the opposite, in the core-enriched model, bigger the particles, higher the EE. If curcumin is located in the corona, higher the specific surface area is, higher the amount of curcumin should be. For spherical particles, the specific surface area is directly proportional to the inverse of the diameter. The evolution of the EE over the estimated SLN specific surface area is presented on Fig. 2.B.

Interactions between the curcumin polar groups and the hydrophilic part of the surfactants molecules could favor the presence of the polyphenol on the outer shell of the lipid nanoparticles and explain why the EE was more important when the surface area increased. To support the hypothesis that curcumin was mainly present in a corona at the particle edge and not in the SLN core, DSC and XRD experiments were performed to study the lipid structure and the effect of the polyphenol incorporation on it.

DSC analysis

The curcumin influence on the melting properties of shea butter at non-dispersed state and under SLN form was studied. Corresponding thermograms are presented on Fig. 3. At non dispersed state, both samples without and with curcumin presented an endothermic peak centered at 37 °C (Fig. 5.A). Under SLN form, this melting signal is shifted towards lower temperature with a maximum at 33 °C (Fig. 5.B). This lowering of the lipid melting point at nanodispersed state has been already reported in the literature [START_REF] Bunjes | Effect of Particle Size on Colloidal Solid Triglycerides[END_REF]. This can be explained by the colloidal nature of the lipid. A different crystalline structure of the solid lipid can also explain this difference.

Nevertheless, the main information coming from the DSC experiment was that the addition of the polyphenol did not modify the lipid melting properties whatever the lipid state, non-dispersed or nanodispersed.

X-ray diffraction analysis

The influence of the polyphenol on the lipid organization at long (longitudinal packing) and short distances (crystalline structure) (Fig. 4.A and B) was studied at both non-dispersed and nanodispersed state by X-ray diffraction (XRD). XRD diffractograms recorded at low angles for samples at non dispersed state are presented in Fig. 4.C. This diffraction angle range (1° < 2 < 12°) allowed the determination of the lipid bilayer structure (longitudinal packing) [START_REF] Lopez | Coupling of time-resolved synchrotron X-ray diffraction and DSC to elucidate the crystallisation properties and polymorphism of triglycerides in milk fat globules[END_REF]. Two main configurations are reported in the literature depending on the repetition patterns of the lamellar structure and refers to the number of carbon chains which define the subcell ; i.e double-chain length (2L) and triple-chain length (3L) (Fig. 4.A). The chain packing is deduced from the repetition distance corresponding to the first reflections observed at small angle (double-chain length 2L: 40 -45 Å and triple-chain length 3L: ~ 60 Å) [START_REF] Amara-Dali | Anhydrous Goat's Milk Fat: Thermal and Structural Behaviors Studied by Coupled Differential Scanning Calorimetry and Xray Diffraction. 2. Influence of Cooling Rate[END_REF]. These configurations depended on the fatty acid composition of the lipid mixture. Double chain length structures were indeed formed mainly by saturated fatty acids while the presence of an unsaturation in the carbon chain could lead to the formation of triple chain bilayers (Fig. 4.A). Both 3L and 2L structures were observed for shea butter with specific diffraction lines at 64 (3L 001 ) and 45 Å (2L 001 ), respectively (Fig. 4.C).

Nevertheless, the main conformation was the triple chain length one with at least 7 reflections.

The peak at 64 Å corresponding to the first order of a 3L structure (3L 001 ) was indeed followed by 6 reflection lines around 32, 21, 16, 12.8, 10.7 and 8 Å were related to the second (3L 002 ), third (3L 003 ), fourth (3L 004 ), fifth (3L 005 ), sixth (3L 006 ) and eighth (3L 008 ) orders, respectively. Double-chain packing was also reported form the peaks located at 45, 21 and 15 Å which were related to the first (2L 001 ), second (2L 002 -superimposed with the 3L 003 ) and third order (2L 003 ) of a double chain length conformation. The presence of these two coexisting phases has been already reported for milk fat [START_REF] Lopez | Coupling of time-resolved synchrotron X-ray diffraction and DSC to elucidate the crystallisation properties and polymorphism of triglycerides in milk fat globules[END_REF]. The lowest number of reflections and intensities of these diffraction lines meant that the amount of 2L conformation was lower than 3L in the sample. The formation of 2L and 3L packing was consistent with the composition of shea butter because the main fatty acids were stearic and oleic acids. Diffraction lines detected at wide angles (15° < 2 < 30°) (Fig. 4.D) were related to the lateral packing (or cross-sectional packing) of the alkyl chains of acylglycerols in characteristic subcells (hexagonal , orthorhombic perpendicular ' and triclinic parallel  forms) [START_REF] Arishima | Polymorphism of POS. I. Occurrence and Polymorphic Transformation[END_REF][START_REF] Kalnin | Systematic investigation of lard polymorphism using combined DSC and time-resolved synchrotron X-ray diffraction[END_REF][START_REF] Ueno | Synchrotron Radiation X-ray Diffraction Study of Liquid Crystal Formation and Polymorphic Crystallization of SOS (sn-1,3-Distearoyl-2oleyl Glycerol)[END_REF]. The  form led to one peak located at q values around 21° (4.2 Å). Characteristic '

patterns present three peaks at 20.5° (4.3 Å), 21.5° (4.1 Å) and 23.2° (3.8 Å) [START_REF] Wille | Polymorphism of Cocoa Butter[END_REF]. In this study, the presence of 8 diffraction peaks (shown in Fig. 4.E and reported Table 3) revealed that shea butter was crystallized into a  polymorph as reported for cocoa butter (Table 3) [START_REF] Wille | Polymorphism of Cocoa Butter[END_REF]. More precisely, the shea butter pattern was analogous (peak positions and intensities) to the one corresponding to the form V of cocoa butter (Table 3) [START_REF] Wille | Polymorphism of Cocoa Butter[END_REF][START_REF] Marangoni | Relationship between Crystallization Behavior and Structure in Cocoa Butter[END_REF][START_REF] Schenk | Understanding the structure of chocolate[END_REF].

The lipid crystalline structure after curcumin encapsulation inside the nanoparticles can bring informations on the localization of the polyphenol in the lipid matrix (shift of the repetition distances, modification of the peak intensities, different crystal structures, etc.) The curcumin influence on the lipid structure was firstly studied at non-dispersed state without water and surfactant at low angles (Fig. 4.C and D). Thus, the structures of pure shea butter and shea butter with curcumin at its maximum solubility (0.33 mg.g -1 , see previous section) were studied. The presence of the curcumin inside the lipid matrix did not strongly modify at first sight the diffraction signal. Similar diffractograms were indeed recorded for sample with and without curcumin (Fig. 4.C). Curcumin did not affect thus significantly the longitudinal chain packing of the lipid (2L and 3L longitudinal packings). In order to go further on the characterization of the lipid 13 longitudinal conformation and to obtain more accurate information, small angles XRD experiments (1° < 2 < 4°) were performed on the same systems (Fig. 4.D). Only the three first diffraction peaks were observed in this 2 range corresponding to the 3L 001 2L 001 and 3L 002 reflections. A closer look on the peak positions revealed that curcumin addition to the lipid led to a shift towards lower angles corresponding to higher repetition distances. 3L 001 reflection was for example shifted from 63.8 Å to 66.1 Å after curcumin addition. This could be related to the presence of the polyphenol between the carbon chains in the lamellar structure leading to an increase of the repetition distance. This increase (2.3 Å for the 3L structure) did not correspond to the curcumin size (close to 16 Å long and 4-5 Å wide) [START_REF] Varshney | Effect of Curcumin on the Diffusion Kinetics of a Hemicyanine Dye, LDS-698, across a Lipid Bilayer Probed by Second Harmonic Spectroscopy[END_REF] but the repetition distances determined by XRD corresponded to an average of the lipid structure. A lower shift towards lower angles was also reported for the double chain length structure. Another difference between the two systems was recorded at low angle (Fig. 4.C) was the peak relative intensities and particularly between 3L 001 and 2L 001 reflections. This could be related to a difference of contrast (modification of the electronic densities) induced by the presence of the curcumin in the lipid structure.

The effect of the polyphenol addition on the crystalline structure of shea butter was also studied at wide angles as shown on Fig. 4.E. Curcumin did not modify the crystalline structure and the  phase was preserved. The only difference between samples with and without curcumin was that the presence of the polyphenol led to broader and less intense peaks. This could be related to a decrease of the crystalline domains size due to the presence of curcumin between them. The peak width depends indeed on the size of the crystallized domain according to the Scherrer's law [32];

(Eq.6)

With D: size of the crystalline domain (Å), K: Scherrer's constant depending on the geometry of the crystal (0.9 if the shape is not known), : X-rays wavelength (1.5418 Å), B: full width at half maximum in °, and : semi-angle of diffraction related to the peak position in °.

Thus, thinner the diffraction peak, larger the domain. From the XRD data recorded for nondispersed samples, it seemed that curcumin was incorporated in the lipid structure. It is also important to notice here that curcumin was not under its crystal form and was really solubilized/dispersed inside the lipid matrix because no additional peaks were reported compares to pure Shea butter. Curcumin XRD pattern indeed showed a lot of diffraction peaks from 10 to 30° (data not shown).

X-ray diffraction experiments was also performed at the nanodispersed state (SLN) with and without curcumin encapsulated in the lipid matrix. The comparison of the XRD patterns at low and wide angles of pure non dispersed shea butter (from Fig. 4.) and at nanodispersed state is presented in Fig. 5. without and with curcumin. At low angle (Fig. 5.A), the more intense reflections (3L packing) reported at non-disperse state were present under SLN form. The lower intensity and the peak broadening were due to the lower amount of lipid in the sample dispersed in water and/or to a lower crystal quality [START_REF] Lopez | Crystallisation of triacylglycerols in nanoparticles[END_REF]. No diffraction lines corresponding to the 2L structure were observed but this could be related to the low intensities of the corresponding peaks. No shift of the peak position after curcumin encapsulation was reported at low angle unlike at non-dispersed state. It seemed that curcumin was not incorporated in the lipid matrix as at nondispersed state. At wide angles (Fig. 5.B), the XRD signature of the lipid lateral packing was strongly different at nanodispersed state than in bulk. The more intense peak of the  phase recorded previously was not present in the patterns and only the reflections at 3.97, 3.87 and 3.69 Å could be related to a  polymorph but with unusual relative intensities. To the best of our knowledge, no analogous diffractograms are reported in the literature. The unusual intensities can be explained by the influence of the nanoparticles form factor which may present a minimum in this 2range leading to a disappearance of the peak at 19.2° and the increase of the intensity of the one at 24.0°. Nevertheless, the main information brought by these experiments was that both diffractograms without and with curcumin are identical. From the obtained results, the addition of curcumin did not affect the lipid structure at nanodispered state unlike at non-dispersed state.

XRD data were thus consistent with the presence of curcumin in the outer shell of the nanoparticles since not difference was reported for sample with and without curcumin. The polyphenol was then not closely included in the lipid matrix and might interact with the surfactants molecules. This kind of interaction was reported in a study focused on the effect of curcumin on phospholipids bilayer properties. Authors reported that curcumin polar groups such as hydroxyl groups might interact with the polar headgroup region of the lipid [START_REF] Varshney | Effect of Curcumin on the Diffusion Kinetics of a Hemicyanine Dye, LDS-698, across a Lipid Bilayer Probed by Second Harmonic Spectroscopy[END_REF]. The curcumin localization inside the nanoparticles was of main importance since it influenced the kind of release. In this case, shea butter nanoparticles favored a burst release of curcumin.

Conclusions

Shea butter solid lipid nanoparticles stabilized by non-ionic surfactants were prepared without the use of organic solvent. The evolution of the nanoparticles size upon system composition was determined using the mixture design methodology. The obtained mathematical models allowed the preparation of SLN of a required size from the system composition. Curcumin, a natural polyphenol, was encapsulated in nanoparticles of several sizes. The encapsulation efficiency was related to the SLN diameter. Bigger the particles, lower the amount of encapsulated curcumin.

From this result, it seemed that the polyphenol was located in the corona of the lipid particle. XRD experiments evidenced that the lipid structure was slightly modified by the curcumin addition at non dispersed state while no differences were detected at SLN state. This was consistent with the fact that the polyphenol was not closely incorporated in the lipid matrix but interacted with the surfactants molecules at the nanoparticles surface which explain the linear decrease of the encapsulation efficiency upon SLN diameter. It was then possible to predict the EE upon the nanoparticles sizes and directly, using the models coming from the mixture design methodology, from the ternary system composition. Experimental q-range is different for SLN samples due to a specific configuration of the apparatus (see materials and methods section 2.g)

Tables

  5-19 wt.% of surfactant. SLN diameter (from the intensity weighing size distribution) and polydispersity index obtained from 23 experiments are presented in Table 1. Particles size distributions obtained from dynamic light scattering measurements of two different systems are presented on Fig. 1.A. Only the formulation composition varied between both samples. The SLN diameter varied from 70 nm to more than 1 µm over the 23 experiments. Fig. 1.B and C present the SLN sizes and related polydispersity index (PdI) responses according to the formulation composition. From a qualitative

Figure 1 :

 1 Figure 1: (A) Size distribution of two nanoparticles (experiments 7 (dotted line) and 9 (full line)), (B) experimental range and variation of the particles hydrodynamic diameter (C) and Polydispersity Index (PdI) (D) responses as a function of the formulation composition.

Figure 2 :

 2 Figure 2: Evolution of the curcumin encapsulation efficiency upon (A) nanoparticles diameter and (B) calculated specific surface area. Experiments have been done in triplicate.

Figure 3 :

 3 Figure 3 : DSC thermograms of shea butter without (continuous line) and with curcumin (dashed line) at (A) non dispersed state and (B) at SLN state. Curcumin content corresponded to its maximal solubility in the lipid.

Figure 4 :

 4 Figure 4: Representations of the solid lipid organization: (A) at long distances (longitudinal packing), double chain and triple chain length configurations detected at small angles and (B) at short distances, crystalline structure detected at high angles (top and longitudinal view of a  triclinic phase). XRD patterns of Shea butter without (bottom line) and with curcumin (top line) at non dispersed state recorded at small (C and D) and (E) high angles.

Figure 5 :

 5 Figure5: (A) Low and (B) wide angles diffraction patterns of Shea butter at non dispersed state (bottom line) at SLN state (middle line) and SLN state with curcumin (top line). Experimental q-range is different for SLN samples due to a specific configuration of the apparatus (see materials and methods section 2.g)

  4090.x Sb -46*.x w + 7263.x s + 9824.x Sb. x w + 22834.x Sb .x s -8078.x w .x s -65365.x Sb .x w .x s Sb + 0.35***.x w + 10.85*.x s -2.22.x Sb. x w -22.69.x Sb .x s -13.41.x w .x s + 1.49.x Sb .x w .x s

	R 2 = 0.86	(Eq.3)
	PdI = 2.65*.x R 2 = 0.90	(Eq.4)

Table 1 :

 1 Mixture design plan of 23 shea butter nanoparticles formulations SLN diameter is expressed in intensity

	N o .exp.	Shea butter fraction	Water fraction	Surfactant fraction	Diameter * (nm)	Polydispersity Index (PdI)
	1	0.05	0.76	0.190	84	0,21
	2	0.40	0.58	0.015	408	0,48
	3	0.05	0.92	0.030	150	0,23
	4	0.06	0.92	0.015	305	0,31
	5	0.40	0.48	0.120	304	0,26
	6	0.33	0.48	0.190	208	0,15
	7	0.05	0.84	0.110	72	0,22
	8	0.19	0.62	0.190	265	0,26
	9	0.23	0.75	0.015	301	0,26
	10	0.40	0.53	0.067	1094	0,80
	11	0.05	0.92	0.022	1624	0,60
	12	0.36	0.48	0.150	201	0,16
	13	0.21	0.69	0.093	871	0,50
	14	0.13	0.72	0.140	470	0,42
	15	0.30	0.63	0.054	316	0,40
	16	0.13	0.8	0.061	214	0,20
	17	0.14	0.8	0.050	193	0,18
	18	0.30	0.58	0.100	170	0,18
	19	0.27	0.58	0.140	419	0,19
	20	0.10	0.87	0.020	189	0,17
	21	0.20	0.76	0.017	194	0,27
	22	0.30	0.68	0.038	203	0,26
	23	0.40	0.57	0.028	204	0,35

*

Table 3 :

 3 Wide angle reflections measured for shea butter compared to cocoa butter  polymorph (form V) from ref[START_REF] Wille | Polymorphism of Cocoa Butter[END_REF]

		Shea butter	Cocoa butter
	2 (°)	Short spacing	Short spacing	Intensity
		(Å)	(Å)
	16.33	5.41	5.40	m
	17.29	5.11	5.15	w
	19.25	4.59	4.58	vs
	-	-	4.23	vvw
	22.10	4.00	3.98	s
	22.71	3.89	3.87	w
	23.43	3.77	3.75	s
	24.00	3.68	3.67	s
	26.28	3.39	3.39	vw

vvw: very very weak ; vw: very weak ; w: weak ; m: medium ; s: strong ; vs: very strong

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Acknowledgement

Authors would like to thanks Carole Jeandel and Carole Perroud for their help during experiments. This study was supported by grants from Erasmus Mundus (Program ELEMENT), Region Lorraine and Université de Lorraine (Program Nutralor). All of these are gratefully acknowledged.

The authors have declared no conflict of interest.