Marie Destandau
email: marie.destandau@inria.fr

Caroline Appert
email: caroline.appert@lri.fr

Emmanuel Pietriga
email: emmanuel.pietriga@inria.fr

S-Paths: Set-Based Visual Exploration of Linked Data Driven by Semantic Paths

Keywords: Visualization, Linked Data, Browser : 0.95 P4 score : 0.84 P28 score : 0.75 P27 score : 0.5 P12 score : 0.43 P38 score : 0.43 P5 score : 0.31 Constraint 3 : 6 matching paths P35 score : 0.7 P1 score : 0.65 P13 score : 0.5 P27 score : 0.44 P4 score : 0.29 P11 score : 0.21 x-axis / dimension 1: P34 y-axis / dimension 2: P35 P34, P4, P28, P27, P12, P38, P5 P35, P1, P13, P27, P4, P11

Meaningful information about an RDF resource can be obtained not only by looking at its properties, but by putting it in the broader context of similar resources. Classic navigation paradigms on the Web of Data that employ a follow-your-nose strategy fail to provide such context, and put strong emphasis on first-level properties, forcing users to drill down in the graph one step at a time. We introduce the concept of semantic paths: starting from a set of resources, we follow and analyse chains of triples and characterize the sets of values at their end. We investigate a navigation strategy based on aggregation, relying on path characteristics to determine the most readable representation. We implement this approach in S-Paths, a browsing tool for linked datasets that systematically identifies the best rated view on a given resource set, leaving users free to switch to another resource set, or to get a different perspective on the same set by selecting other semantic paths to visualize.

Introduction

Linked Data browsers face a complex problem. They are expected to display any RDF data [START_REF] Karger | The Semantic Web and End Users: What's Wrong and How to Fix It[END_REF] so as to enable users to effectively explore an open web of datasets whose structure is inherently complex and whose content can be highly heterogeneous, featuring a wide variety of resources described by classes and properties from multiple ontologies.

Most linked data browsers employ a follow-yournose strategy inherited from the classic Web browsing paradigm: they display one page per RDF resource, fetching its direct properties and allowing users to hop in the graph one step at a time by clicking on property values when those can be dereferenced (URI) [START_REF] Steer | BrownSauce: An RDF Browser[END_REF][START_REF] Koch | LENA -Browsing RDF Data More Complex Than Foaf[END_REF]. This strategy scales well in terms of performance, enabling users to traverse an arbitrary number of linked datasets regardless of their size. The representation of resources is as meaningful as it can be in the absence of vocabulary-specific display instructions [START_REF] Pietriga | Fresnel: A Browser-independent Presentation Vocabulary for RDF[END_REF], i.e., spatial and temporal properties can be displayed in maps, calendars or timelines, while most other prop-erties will be handled in a generic manner, typically as lists of property-value pairs. Automatically generating more meaningful representations of resources and their properties is challenging, and remains an open research problem. The challenge, however, does not only lie in the difficulty to find such meaningful representations. It also lies in identifying what properties provide meaningful descriptions of resources in the first place, and in putting those resources in the broader context of similar resources.

Properties that provide relevant descriptions of resources are not necessarily direct properties of those resources. They can be several hops away in the RDF graph, depending on the granularity of the model. For instance, considering the Nobel prize dataset, 1 key information about laureates is the prize category (3 hops) and the year of award (2 hops). Follow-your-nose navigation is ill-suited to this, as it puts much cognitive burden on users: reaching the property of interest requires several clicks, hopping from page to page and loosing the context of the original resource. Keeping the chain of previous pages in mind requires a significant mem-orization and integration effort. It can be compared to having to express facts using a chain of basic sentences -Peter has a son / the latter has a nephew / the latter has a wife / the latter is a pharmacist -instead of being able to express them in a single sentence -The nephew of Peter's son is married to a pharmacist. The associated mental effort increases as users browse back and forth to explore other paths, making the follow-yournose approach impractical.

Our approach is rather to remain at the original resources of interest; to identify particular chains of statements, which we call semantic paths, that lead to meaningful descriptions of those resources; and to display the values at the end of those paths using an appropriate visualization. This not only addresses the above problem of original-resource context loss, but also enables displaying semantic paths for sets of resources all at once, thus easing their comparison. For instance, going back to the analogy used above, this enables comparing the spouse's occupation for all the relatives of Peter's children.

But considering all properties up to a given depth in the graph can yield a large number of candidate semantic paths, even for a single resource. And considering sets of resources can yield a large number of distinct values, even for a single semantic path. The amount and heterogeneity of information to display can thus rapidly become quite large. To address this issue, we rely on the automatic selection of which semantic paths to display by default, and on aggregation techniques to generate legible visual representations of the values at the end of those paths.

We argue that providing users with such default, possibly aggregated, views is an efficient strategy for browsing datasets, especially in situations where users are unfamiliar with them (dataset discovery). We implement this approach in S-Paths, a prototype Webbased system that can be plugged on SPARQL endpoints, which we evaluate with different persona (data publishers, data reusers, lay data consumers) to gather feedback about the effectiveness of the approach and general user experience with the tool.

Related work

A review of all linked data browsers and visualization tools is beyond the scope of this paper. We direct readers to recent surveys [START_REF] Bikakis | Exploration and Visualization in the Web of Big Linked Data: A Survey of the State of the Art[END_REF][START_REF] Dadzie | Approaches to visualising Linked Data: A survey[END_REF][START_REF] Dadzie | Visualisation of Linked Data -Reprise[END_REF], and only discuss representative examples of the different approaches related to S-Paths.

Early visualization tools exposed the raw RDF graph represented as a node-link diagram [START_REF] Pietriga | IsaViz: a Visual Environment for Browsing and Authoring RDF Models[END_REF], sometimes using stylesheets to customize the appearance of nodes and links [START_REF] Pietriga | Semantic Web Data Visualization with Graph Style Sheets[END_REF]. The approach is generic, and the resulting representations can be useful to illustrate very small graphs and communicate to a relatively expert audience, but it quickly yields illegible "big fat graphs" [START_REF] Schraefel | The Pathetic Fallacy of RDF[END_REF]. In most cases, regardless of the graph drawing technique used to generate the visualization, the RDF graph is not the right level of abstraction for presentation purposes [START_REF] Dadzie | Visualisation of Linked Data -Reprise[END_REF]. It is often quite verbose and the details of how the model structures the data are often of low interest to users browsing the Web of Data. Three systems that display the data primarily as node-link diagrams, but at a higher level of abstraction than the raw RDF graph, and for specific purposes, are LodLive [START_REF] Camarda | Exploring the Web of Data[END_REF], Visor [START_REF] Popov | Connecting the Dots: A Multi-pivot Approach to Data Exploration[END_REF] and RelFinder [START_REF] Heim | RelFinder: Revealing Relationships in RDF Knowledge Bases[END_REF]. The first two limit visual clutter by using a dynamic graph and using aggregation, expanding nodes and links on demand; the latter focuses on showing paths connecting pairs of resources only, starting with the shortest ones. Visor also helps identify paths connecting elements several hops away in the graph structure, taking edge direction into account.

Linked data browsers break free from the node-link diagram to consider a wider range of visual representations. The first browsers, such as Brownsauce [START_REF] Steer | BrownSauce: An RDF Browser[END_REF], produced generic (almost raw) representations of the data in HTML pages, exposing property-value pairs of the current resource of interest as text and clickable URIs. Clicking a URI would attempt to dereference it, and a new HTML page with the properties of the corresponding resource would be displayed. They dynamically generated HTML pages showing RDF triples in a generic manner, with some basic formatting to improve readability. Follow-up work, including LENA [START_REF] Koch | LENA -Browsing RDF Data More Complex Than Foaf[END_REF] and the Marbles engine [START_REF] Becker | Exploring the Geospatial Semantic Web with DBpedia Mobile[END_REF], used presentation knowledge captured in vocabulary-specific Fresnel lenses and formats [START_REF] Pietriga | Fresnel: A Browser-independent Presentation Vocabulary for RDF[END_REF] to enhance the representation. Such languages, however, require that declarative presentation rules be available to the browsers for the different RDF vocabularies involved. Some of them also supported map-based or timeline-based visualizations for spatio-temporal properties, culminating in the Tabulator [START_REF] Berners-Lee | Tabulator: Exploring and analyzing linked data on the semantic web[END_REF] which, despite being more than a decade old, remains one of the most ambitious projects in this area so far, also aiming at making the Web of Data writable [START_REF] Berners-Lee | Tabulator Redux: Browsing and Writing Linked Data[END_REF]. However, since Tabulator only features a limited set of views (map, timeline, calendar), it frequently displays data using a generic, more triple-oriented, tree or tabular view on data which are neither spatial nor temporal.

While the above are primarily supporting exploration one resource at a time, other systems based on advanced query mechanisms, such as Visinav [START_REF] Harth | VisiNav: A system for visual search and navigation on web data[END_REF], or more specifically based on faceted browsing, such as /facet [START_REF] Hildebrand | /facet: A Browser for Heterogeneous Semantic Web Repositories[END_REF], provide support for particular types of setbased navigation [START_REF] Popov | Connecting the Dots: A Multi-pivot Approach to Data Exploration[END_REF][START_REF] Huynh | Parallax and Companion: Setbased Browsing for the Data Web[END_REF]. But as observed by Marie and Gandon [START_REF] Marie | Survey of linked data based exploration systems[END_REF], the often large number of facets, combined with the irregularity and incompleteness of semi-structured data on the Web, tends to result in cluttered, unusable interfaces. The problem can be alleviated by enabling users to select facets on the fly [START_REF] Hildebrand | /facet: A Browser for Heterogeneous Semantic Web Repositories[END_REF], and help them determine their relevance [START_REF] Tzitzikas | Faceted Exploration of RDF/S Datasets: A Survey[END_REF]. But such approaches require users to make choices about facets. Another limitation of existing facet-based exploration systems lies in how they display results, i.e., as lists of items in most cases (presented as text or image thumbnails). These can sometimes be complemented with aggregated views in the form of maps or timelines, which are familiar, graspable views [START_REF] Petrelli | Multi Visualization and Dynamic Query for Effective Exploration of Semantic Data[END_REF]. But even then, the types of visualizations available is limited. Set-oriented tasks, such as identifying correlations, observing distributions, comparing & contrasting groups of resources, remain difficult.

Answering questions such as these, and more generally gaining insights about collections of resources, requires generating multi-variate data visualizations (e.g., scatterplots [START_REF] Heim | SemLens: Visual Analysis of Semantic Data with Scatter Plots and Semantic Lenses[END_REF]) of a set of properties associated with resources in the set. The Linked Data Visualization Model [START_REF] Brunetti | Formal Linked Data Visualization Model[END_REF] defines a transformation workflow to dynamically associate one or more datasets with multiple visualizations. Implementations of this workflow typically support a range of data visualization techniques. The methodology defined in [START_REF] Braşoveanu | Visualizing statistical linked knowledge for decision support[END_REF] focuses on statistical linked data as found in, e.g., RDF data cubes, making it possible to combine data from different linked sources and display them in visualization dashboards. Multiple other projects have been attempting at making it easier for users to generate data visualizations from linked data. Again, the reader is referred to recent surveys [START_REF] Dadzie | Approaches to visualising Linked Data: A survey[END_REF][START_REF] Dadzie | Visualisation of Linked Data -Reprise[END_REF] for an exhaustive list. Of particular interest here are Visualbox [START_REF] Graves | Creation of Visualizations Based on Linked Data[END_REF] and Link-DaVis [START_REF] Thellmann | LinkDaViz -Automatic Binding of Linked Data to Visualizations[END_REF]. Visualbox enables its users to create different visualizations by writing SPARQL queries and populating predefined visualization templates with the queries' results. The produced visualizations can then be embedded in classic Web pages. LinkDaVis provides users with a hierarchical representation of properties, from which users can choose the ones to visualize. It then performs a heuristic analysis of the data to suggest a ranked list of visualization configurations for these properties, based on different bindings to visual encoding channels. Once a particular visualization is selected, it can further be customized, as in other mixed-initiative approaches such as that adopted in Voyager [START_REF] Wongsuphasawat | Voyager: Exploratory Analysis via Faceted Browsing of Visualization Recommendations[END_REF], a tool for the creation of multi-variate data visualizations.

Such tools are very powerful, and enable the creation of a wide variety of visualizations from linked data: maps, timelines, and a range of statistical charts (scatterplot, line plot, density plot, etc.). However, they produce standalone visualizations, that can be used on the spot or exported and integrated elsewhere. They don't support browsing over the Web of Data. Indeed, once created, these visualizations feature a very limited level of interactivity. They cannot be used directly to make sub-selections or continue navigation, which requires following links, fetching additional data, and displaying it.

S-Paths

S-Paths is a mixed-initiative application [START_REF] Thellmann | LinkDaViz -Automatic Binding of Linked Data to Visualizations[END_REF][START_REF] Wongsuphasawat | Voyager: Exploratory Analysis via Faceted Browsing of Visualization Recommendations[END_REF] designed to support users in the exploration of linked datasets, providing them with visual representations of resource sets that help gain insights about those resources. Users can adopt different perspectives on the data: focus on a subset of interest, select different types of view, display other dimensions, pivot to a set of related resources. This section first describes how S-Paths defines semantic paths, views, and how it matches them. It then describes a prototype user interface based on this approach.

Semantic Paths

We introduce the concept of semantic paths. We denote U the set URIs and L the set of literals, as is usually done in the literature to define RDF terms. Given an RDF graph G, and a set of resources E sharing a similarity criterion such that: Given a set of resources, S-Paths considers all semantic paths to identify those that can be matched with its visualization templates, presented in Table 2. Each template declares the category of paths it is able to display, and the optimal and limit conditions for readability. S-Paths uses a set of heuristics to rank the views and displays the best ranked one by default. Considering paths representing chains of triples, and not only direct properties, gives more opportunities to find properties that are in a displayable range.

∀e 1 , e 2 ∈ E ⊂ U, ∃ C ∈ U,
We define categories corresponding to different behaviors in terms of aggregation and display, and conceptually roughly equivalent to datatypes. Datetimes can be aggregated by years, decades, centuries...; geographical coordinates can be aggregated at different scales, as on multi-scale maps; images can be resized, displayed at different scales, and juxtaposed in grids or mosaics; numbers can be binned; text strings can only be aggregated by similar values, and can be displayed according to different layout strategies depending on their length; URIs can only be aggregated by similar values. These categories are very similar to the ones used by Atemezing and Troncy [START_REF] Atemezing | Towards a Linked-Data based Visualization Wizard[END_REF].

The main characteristics considered are summarized in Table 1. Depth captures the degree of indirectness of the property at the end of a path (i.e., the semantic path length, or number of hops to reach it from the original resource). Coverage indicates the percentage of entities actually described by the path. This notion of coverage is especially important in the context of semi-structured data, where no schema is enforced and some properties exist for only a subset of all considered resources.

Path analysis is performed when S-Paths gets set up with a new set of graphs, and the characteristics are stored in a Mongo database, which will be retrieved by the system when users navigate. The query to characterize the paths can be formalized as in Figure 1. However, running such a query is very likely to time out, except with very small datasets. S-Paths splits it into multiple queries, following a divide-and-conquer strategy. The analysis function takes as input a set of paths, and the similarity criterion for the entities. For each path of maximum length in the set of paths, it queries all extensions by appending one property at the end.

Then for each new path found, it queries separately for coverage and count, and datatype information, as shown in Figure 2. Then the analysis function saves its results, and calls itself recursively until the maximum length of paths set in the configuration is reached. This allows to progress in the exploration step by step, and to resume where it stopped if the network or SPARQL endpoint breaks.

View Specification

S-Paths provides a set of views: map, image gallery, timeline, statistical charts, simple node-link diagrams, presented in Table 2. Each view specifies how many dimensions it can handle, and defines the requirements that semantic paths must meet to be considered for a given dimension, as well as the conditions under which they will be considered optimal. For example, Figure 3 shows the definition of a 2D density plot view. It handles two dimensions: x-and y-axis. Paths associated with the x-axis (dimension 1) must be of category datetime, text or URI. If the category is datetime, the number of distinct values (unique count) is not limited as they can be aggregated meaningfully (line 8). On the contrary, if the category is text, the unique count must not exceed 150 (line 9).

Each view also receives a weight. Generic views, that are able to handle any data, can be lower rated, while very specific views able to give a more meaningful representation but only for specific types of data can be given higher priority. Petrelli et al. [START_REF] Petrelli | Multi Visualization and Dynamic Query for Effective Exploration of Semantic Data[END_REF] refer to space, time and topology as examples of graspable dimensions that provide effective support to the exploration and sense-making of semantic data. Indeed, the aggregation mechanism is embedded in the map background and in our mind, which explains why they scale so well: when we look at a world map we automatically think in terms of continents, while when we look at a zoomed map we think in terms of countries or region. Our mind seems to be continuously looking for the most graspable dimension, which is probably why Bertin states that "Useful information comes with clusters" [START_REF] Bertin | La graphique et le traitement graphique de l'information[END_REF].

This also makes it possible to have various levels of overview, depending on the number of items in the selection when dealing with very large sets. The system should support, and default to, aggregate views on the data, enabling users to easily select subsets of higher interest to focus on, eventually displaying them in detail [START_REF] Shneiderman | The Eyes Have It: A Task by Data Type Taxonomy for Information Visualizations[END_REF] when the set size becomes tractable.

Matching Algorithm

Once semantic paths for a given resource set have been retrieved, the system evaluates the suitability of the different views to generate a default representation of this resource set. Figure 5 gives an overview of the process. S-Paths iterates through the entire collection of views, discards the ones that are not viable for the set of resources considered, configures the remaining ones with the top-ranked semantic paths as dimen- sions, and gives a score to each candidate view, eventually selecting the top-ranked one.

Some views define a maximum number of resources they can handle. When the number of resources to visualize exceeds that maximum number, this view is discarded. Otherwise, S-Paths computes the list of candidate paths for each of the view's dimensions. If there is no path matching the constraints for one of the dimensions, the view is discarded. S-Paths assigns a score to each path, using a normalized weighted average of the following criteria:

path coverage: S-Paths favors paths that have a high level of support (cover a large number of resources); adequation between the path and the view dimension: a path closer to the optimal settings for a dimension is scored higher. A dimension can specify optimal settings in terms of unique count (Figure 3, lines 8-10 and 13-14), and in terms of average char length (avgcharlength) for paths leading to textual values. Also, the closer to the ranges defined as optimal for the dimension, the better the score. When a dimension supports several categories, it lists those categories in order of preference. This preference influences the score. For example, in ranked paths that still match this view can be selected using the dimensions menus. The view menu lets users switch to any other view available for the resource set.

When users select a subset, the system retrieves paths for the entire set, and computes an approximation for the subset.

SPARQL query mechanism

S-Paths' query mechanism is independent from any view specifics. It switches between three possible query templates according to the type of view -aggregate view, multiple distinct entities, or single entity -as detailed in Figure 4. In the case of aggregate views, binning operations are performed in the query for paths belonging to datetime, geo or number category, so as to ensure the number of results will not exceed the endpoint quota (lines [START_REF] Berners-Lee | Tabulator: Exploring and analyzing linked data on the semantic web[END_REF][START_REF] Berners-Lee | Tabulator Redux: Browsing and Writing Linked Data[END_REF]. Queries which handle transitions between views are identical, combining dimensions from the previous and the new view.

When a subset is selected in an aggregate view, constraints to define the subset (lines 11-12 or 31-32) are added to the ones already gathered in previous views. When the selection happens in a multiple distinct entities view, previous constraints are replaced by the list of selected URIs. When users pivot to explore another set of resources, constraints defined in previous views are rewritten: ?entities is renamed ?oldentities, and the relation between ?entities and ?oldentities is added.

Configuration

S-Paths requires minimal configuration: the URIs of the SPARQL endpoint and of the named graphs to explore behind it. At start up the system looks for rdf:type statements in those graphs, and displays a list of classes which can be analyzed. A configuration file enables to adjust other optional parameters, in order to adapt the system to a specific dataset: the maximum length of the paths, the weight of the different criteria used in the matching algorithm, and the prefixes (namespace bindings) for URIs.

User Interaction

The system then provides them with different options as entry points into the data, which correspond to the different types of entities detected (classes of resources). By default, it selects the class of resources that has the richest description, and generates a default view that acts as a gateway to that set of resources.

Figure 9-a shows the interface when starting to browse the earlier-mentioned Nobel prize dataset. It is composed of a set of widgets in the upper part, and a central panel showing a visualization of the resource set. S-Paths has selected the Award class of resources as the entry point. The resource set containing more than 1,500 awards, the system defaults to an aggregate visualization (the color of individual cells encodes their element count), selecting the award's year and its category as the two dimensions to display. S-Paths displays summary information about the resource set and the visualized semantic paths just above the view itself, providing users with some context (see, e.g., Figure 9-a). Detailed information about the selected semantic paths and the RDF graphs they traverse is also available. Such provenance-related information is especially useful when dealing with heterogeneous datasets distributed over multiple linked graphs, but as it is rather expert-oriented, it gets displayed on demand only, by clicking an icon [ ] next to the summary.

From a presentation perspective, S-Paths seeks to display user-friendly labels for the resources and properties encountered along semantic paths. The corresponding URIs are systematically dereferenced, looking for labels and descriptions (rdfs:label, etc.). These are used in the interface: next to the resource selection menu, in the view configuration menu, in the axes' legends, and whenever a semantic path is displayed in a view template. When no label can be found, the system falls back to the prefixed URI using the prefix.cc Web service.

Resource Set Selection

Users can select another resource set in the top row of the UI. They can switch to any other class available in the menu. Available classes of resources correspond to the sets of instances that share a particular class (rdf:type statements. For example, Figure 6-a shows the default view when the Laureate class is selected. Users can further refine the resource set by specifying a in the form of keywords to be matched in values anywhere along the associated semantic paths. Users can use such a filter to restrict the initial Laureate set (910 resources) to laureates related to keyword medicine (217 resources).

View Configuration

The drop-down menus in the second row of the UI (dimensions menus) let users change which semantic paths get visualized in the view. They support autocompletion for quick selection in the list. The number of dimensions menus depends on how many dimensions the view expects. For instance, the default view generated by S-Paths for the Award class is a histogram (Figure 6-a) showing the distribution by award year (horizontal axis) and by gender (color). The user can change the semantic paths set in the two dimensions menu. In Figure 6-b, the histogram has been reconfigured to show the distribution by birth date and by category. Each menu only features paths whose values are of a type compatible with the associated dimension in the chart. For instance, on a map view, the first two menus, which correspond to the latitude and longitude of items to be plotted, will only feature semantic paths that point to geo-location properties such as, e.g., wgs84_pos:lat and wgs84_pos:long. Similarly, the timeline view will only allow semantic paths ending with time-related properties for its first dimension. Users can also choose another type of visualization using the view menu , which lists all vi- sualizations compatible with the current resource set (chart, timeline, map, image gallery, etc.). Selecting a different visualization in this menu will generate a new view based on the top-ranked semantic paths for that view. For example, in Figure 6-c, the user has selected the map view. S-Paths automatically populates this view with longer, three-step semantic paths:

dbpedia:birthPlace/owl:sameAs/wgs84_pos:lat, dbpedia:birthPlace/owl:sameAs/wgs84_pos:long.

Subset Selection

The above view reconfiguration capabilities let users change what dimensions of resources in the current set are visualized, and how they are visualized. Users can also restrict what resources to visualize by making direct selections in the currently displayed view: clicking on individual items and aggregates, performing rubber-band selections of contiguous elements, selecting ranges by, e.g., clicking a particular bin on the horizontal axis of a histogram to select all items in that bar. They can also combine multiple, non-contiguous selections by holding a modifier key (Shift), as in popular graphics-oriented applications such as presentation programs and graphics editors. Once such a subselection has been made, users can turn it into the new resource set to explore. The process can be repeated iteratively. Combined with the automatic aggregation of resources along the chosen dimensions, which only occurs when the resource set is too large, this selection mechanism provides users with means to effectively zoom-in on part of the data and get details on demand [START_REF] Shneiderman | The Eyes Have It: A Task by Data Type Taxonomy for Information Visualizations[END_REF]. For example, starting from the map in Figure 6-c, it is possible to select laureates in South America and Africa only, and focus on them.

The two percentage bars in the top right corner of the interface give an indication of what proportion of the dataset is currently visualized. The upper bar indicates how many resources of the selected type match the . The lower bar indicates how many resources of the selected type are actually represented in the main view. This latter set of resources depends on the successive user selections, and on the selected semantic paths, that might not exist for all resources in the current set.

Navigation and Transitions between Views.

S-Paths smoothly animates transitions between views when the two views have entities in common [START_REF] Heer | Animated Transitions in Statistical Data Graphics[END_REF]. This provides some basic level of perceptual continuity that contributes to minimizing the cognitive cost of relating one view to the next, as illustrated in Figure 7. Visual marks that represent aggregations of resources are partitioned according to a space-filling strategy. This preserves aggregations that still exist in the target view and might actually be part of a larger aggregate.

The system also supports the juxtaposition of two consecutive views, as well as brushing and linking between those views: selecting elements in one view immediately highlights the corresponding elements in the other view (see Figure 8), further helping users relate views. The same space-filling strategy as above is used to handle brushing & linking between aggregates.

S-Paths also keeps track of all past views and represents them as dots forming a basic navigation history displayed in the bottom left corner of the interface. Clicking on one of these dots reverts to the corresponding view, enabling users to easily backtrack.

Transitioning from one view to another requires an explicit user action in S-Paths. Users have to click button to focus on a subset selection, or one of the buttons to apply other configuration changes. While an explicit user action is necessary to offer the multiple-selection model described above, configuration actions would preferably not require users to explicitly apply changes, in order to promote responsiveness and immediate feedback. But, as changes to the resource set and to the view settings can take several seconds (depending on the complexity of the underlying SPARQL queries, on the size of the resource set considered, and on the overall responsiveness of the queried endpoints), this is impossible in practice. Triple store query performance needs to improve by at least an order of magnitude before this can be seriously considered.

Pivot

Switching to another set of resources related to the current set is an essential operation in set-based navigation. The classic example of such a pivot operation can be found in Parallax [START_REF] Huynh | Parallax and Companion: Setbased Browsing for the Data Web[END_REF] where focus switches from all presidents of the USA to the children of presidents affiliated with the Republican party. In S-Paths, clicking lists all possibilities for pivoting from the current view. These include root pivots, and path pivots. Root pivots are other classes that entities in the current resource set itself may belong to (multiple rdf:type values). For instance, in Figure 9-a, nobel:LaureateAward and nobel:NobelPrize are listed as options for pivoting, as some entities in the current resource set (dbpedia-owl:Award) also belong to one or both of those classes. Choosing e.g., the nobel:NobelPrize pivot will select the set of resources from the current view that belong to the nobel:NobelPrize class. Path pivots are sets of resources found on the semantic paths used as dimensions in the view. For example, path nobel:category/rdfs:label is used as the second dimension in the view (Figure 9-a); nobel:Category thus gets listed as the third option for pivoting. In all cases, pivoting takes into account subselections made by users in the view. For instance, selecting the column corresponding to the 1940's in Figure 9-a and pivoting to Category would lead to a view showing only 5 out of all 6 categories, as the prize in Economic Sciences was established in 1968.

Implementation

S-Paths is developed using NodeJS/Express. RDF data is stored in a Virtuoso instance, and queried using SPARQL. Semantic paths are encoded using the Fresnel FSL syntax [START_REF] Pietriga | Fresnel: A Browser-independent Presentation Vocabulary for RDF[END_REF]. The code analyzing them runs server side, storing their characteristics in MongoDB.

When populating a view, S-Paths only fetches the data actually displayed in the view, so as to improve scalability and support browsing large sets of resources. It queries the SPARQL endpoint using query patterns that retrieve only the distinct values at the end of the property paths.

The front-end is implemented as a Single Page Application developed with React and Redux, a React component being associated with each view. Views are implemented in a modular way, so as to ease the process of extending S-Paths with new types of views. New views have to implement a minimal interface to fit in the general framework: publish their constraints on allowed dimensions; broadcast subset selections made by users in the view; and broadcast graphical properties of the entities they display to enable interpolated graphics transitions, as well as brushing & linking between views. Beyond this, each view is free to handle the data in its own way: clustering and other aggregation methods, library used for graphics rendering (many views are implemented with Vega [START_REF] Satyanarayan | Reactive Vega: A Streaming Dataflow Architecture for Declarative Interactive Visualization[END_REF], others are plain HTML+CSS), etc.

S-Paths is distributed as an open-source project2 . The demo instance3 runs on a Linux virtual machine with 4 vCPUs, 16GB RAM, 32 GB disk space. This demo currently runs on a single Virtuoso instance, using the default configuration.

Illustrative Scenario

This section illustrates how S-Paths works using a simple scenario. We follow Alice, a lay user interested in the data made available by the Nobel Prize organization. We will see how S-Paths enables her to find interesting facts. The first screen displayed by S-Paths is a 2D density plot showing information about Awards: their category and year (Fig. 9-a).

Alice notices that five of the six categories start at the beginning of the 20th century, while the sixth, Economic Sciences, was only created in the 1960's. From the colors in the cells, she sees that disciplines such as Physics and Medicine have more awards than, e.g., Literature. She wonders if she can find an explanation, which prompts her to try other dimensions than year for the horizontal axis.

Using the first dimension menu, Alice considers different options. Hovering the different property paths, she can read their description. She finds the share property (Fig. 9-a), which corresponds to the number of shares a prize is divided into. She selects it. This displays the view in Fig. 9-b, which reveals that awards in the Literature category (3rd row from top) tend to have a lower share value (often 1, sometimes 2) compared to those in the other categories (more evenly distributed between 1 and 4). She now understands why the number of Awards is higher in scientific disciplines: prizes are mostly given to two-to-four people in the latter case, while they are often given to a single person in Literature.

Alice would like to know more about Laureates in Literature. She selects that line in the view and asks S-Paths to focus on it. Looking at the resulting stacked chart, she is struck by the unbalanced distribution between men and women (Fig. 9-c). She reconfigures the view to get a map, displaying the geographical origin of Laureates (Fig. 9-d). She notices that many of them were born in Europe.

Alice wonders if the gender repartition is the same in all categories. Using the top menu, she considers the entire set of Laureates (Fig. 9-e). Her attention is caught by the fact that there is only one Laureate born in the 1990's and that she is a woman. Alice selects this single entity and focuses on it. The generic info card (Fig. 9-f) detailing this Laureate resource reveals that this is Malala Yousafzai, a young Pakistani who was awarded the peace prize in 2014.

Coming back to her original question about gender repartition, Alice goes back to the previous screen (Fig. 9-e), which she reconfigures to display gender and category (Fig. 9-g). She observes that gender unbalance is particularly pronounced in Chemistry, Economic Sciences, and Physics. She selects all female laureates and focuses on them. This yields a timeline view (Fig. 9-h) in which she can read their name, as well as their birth, death and award dates.

Evaluation

In the early design phase of S-Paths, we conducted two workshops in order to inform our design choices. The first workshop involved nine Linked Data experts, and the second one seven lay users (data consumers) who were interested in exploring linked data. We asked them to sketch scenarios of what they would like to be able to do when exploring Linked Data, illustrating how an ideal tool would support them. Feedback from these workshops, combined with informal observations during the French National Library's hackathon and other Linked Data community events in Paris allowed us to derive three persona that represent our target users: a Linked Data PUBLISHER, a Linked Data REUSER, and a LAY USER who seeks information.

At the end of S-Paths' design process, we conducted a qualitative study to observe how S-Paths supports users in their exploration of a dataset. The study consisted of a series of nine individual sessions: 2 PUB-LISHERs, 2 REUSERs and 4 LAY USERs. Each session started with the operator demonstrating S-Paths for ten minutes. Participants then explored a dataset for twenty minutes, and were encouraged to think aloud. Sessions ended with a questionnaire to gather feedback about their experience. Each session lasted an hour.

The exploratory tasks to be performed depended on the persona. Lay users were provided with a list of specific tasks 4 in order not to get them inhibited by the open-ended nature of the task, but the operator made it clear that tasks were indicative, and that participants were free to explore the dataset as they wanted.

Reusers were asked to discover a dataset as if they were in a hackathon: explore a dataset and find a potential application to develop based on these data. Sessions with both lay users and reusers were conducted with the Nobel prize dataset. Publishers were asked to take a fresh look at their own data.

Our hypothesis was that aggregating data along readable dimensions as S-Paths does would help users gather high-level knowledge about a dataset. In particular, S-Paths helps spot outliers (e.g., there is only one laureate born in the 1990's and she is a woman), but also shows categories or trends (e.g., awards in literature are usually not shared). In the rest of this section, we report on our observations along four axes that White & Roth [START_REF] White | Exploratory Search: Beyond the Query-Response Paradigm[END_REF] identify as key aspects for the evaluation of an exploratory search system: learning and cognition, information novelty, engagement and enjoyment. We do not analyse task success and task time, the number of participants being too low to yield significant results.

Learning and Cognition

In order to assess how much users learnt during their use of S-Paths, REUSERs and LAY USERs had to answer a series of five questions about Nobel prizes in the final questionnaire. 5 They also had to tell whether they would have been able to answer those questions before the experiment. All seven participants successfully answered the series of five questions, and would not have been able to do so before the experiment in most cases (1 reuser knew the answer for 3 questions, 1 lay user for 1 question, all 4 other participants knew none of the answers). The questionnaire additionally asked participants to report other facts they had learnt. They all reported learning some facts, ranging from specific ones (e.g., "Marie Curie is the first woman to get an award in 1903" or "Vernon Smith was awarded the only prize in economic psychology") to general ones (e.g., "Many Nobel prizes were born in the UK" or "Organizations can be awarded a prize").

As participants were thinking aloud, the operator noticed that it was not always clear to lay users which entity was represented in a view. However it did not seem to have much impact on their understanding. For example, they might not have known that the view in Figure 9-a was showing the number of Laureate Awards and what the definition of a Laureate Award was. However, it did not prevent them from learning that there were six categories for Nobel prizes, and that prizes have existed for over a century.

Information Novelty

S-Paths makes it easy for users to get views that combine several paths, providing insights that would otherwise have required some analysis. Reusers and publishers were the most enthusiastic about getting such combined views that reveal distributions, trends or outliers in the data. One reuser mentioned that S-Paths automatically does what he typically does by means of multiple SPARQL queries or Python scripts to analyze dumps at the start of a hackathon: "When you engage in a hackathon, what you are looking for is irregularity in the data, and this tool finds them and points them out.".

The two data publishers spontaneously identified specific cases where S-Paths may be very useful. The first data publisher is in charge of the ontology of Legilux, 6 a dataset containing all of Luxembourg's legal texts. He often gets requests for data from the Luxembourg publications office, whose experts need to answer questions coming from the government; or to react to statements made by journalists. Providing those data requires writing SPARQL queries, and importing their result sets into a spreadsheet to generate charts. S-Paths would remove the need to write queries and resort to other tools for data presentation, and would thus greatly improve such a workflow.

The second data publisher is the Bibliothèque nationale de France (BnF). Their data come from multiple catalogs, and are enriched with external data, making it particularly difficult to get an overview of their dataset. They liked the fact that S-Paths provides views that combine metadata with meta-metadata (e.g., a view of works that combines the work's topic with the year when the work was added to the catalog). This helps understand the cataloguing policy and trends, and spot anomalies in the data. In particular, S-Paths could drive campaigns for cleaning and fixing data.

Engagement and Enjoyment

All participants were fully focused on their tasks. Twenty minutes seemed short to them. Lay users were able to use the tool without knowing about graph databases or what a path in a graph is. However, some of them expressed concerns about the interface's responsiveness. For example, they would have expected previews on rollover for any selection before actually validating it. On the opposite, experts understood the underlying computation cost, and were tolerant regarding the non-instantaneous generation of views.

Limitations

User Interaction

Our observational study revealed two aspects of the interface that might negatively impact user experience. The first issue is related to the number of entities that are actually shown in a view. The automatic aggrega-tion and selection of paths might give the impression that the view displays the whole set of entities that has been selected from the previous view. Although S-Paths' scoring strategy favors paths that have a high coverage, the semi-structured nature of data makes it very frequent to have irregularities in the data, and thus partial coverage only. While actual coverage is shown in the top-right corner of the interface, a participant mentioned that it should be made more salient. The second issue was raised by one of our lay users. While she liked the fact that S-Paths automatically selected views, she found it frustrating that the system did not remember the dimensions she had explicitly set when she was revisiting a given set of entities. One way of addressing this issue would be to take into account the navigation history in S-Paths' scoring strategy.

Data Processing

We did set up S-Paths with seven datasets of varying size and with different characteristics: Nobel, 7 Data BnF,8 ELI, 9 RISM, 10 John Peel Sessions, 11 Amsterdam Museum, 12 and Linked Movie DB, 13 revealing a few issues that S-Paths' approach can run into.

First, both ELI and RISM datasets lack rdf:type statements. As S-Paths relies on those statements to list candidate resource sets to start exploring from, we relied on the model to generate and store them in a small adjacent graph.

Second, S-Paths encounters performance issues with the BnF dataset. The high level of abstraction of the model, which makes the relevant paths potentially very long, combined with the very large number of entities, significantly increased the cost of each SPARQL query. This problem could be addressed by implementing mechanisms for query optimization. Furthermore, the granularity of the model resulted in a very large number of paths, some of them having a very low coverage. To keep the matching algorithm reactive, we implemented an ad hoc solution that consisted of restricting the considered paths to the first fifty featuring the highest coverage at the start. A better solution would dynamically update the list of candidate paths whenever users focus on a new subset of resources, as a given path's coverage can vary significantly from one subset to another. This would require implementing advanced graph exploration techniques to identify relevant paths without having to check them all after each new subselection.

Available Views

Finally, in the John Peel Sessions dataset, S-Paths is unable to match paths with any view for several classes of resources. This is because values at the end of the paths consist of mostly-unique URIs or text values. In the current implementation, S-Paths does not provide aggregation mechanisms in such cases. Generic aggregation methods would make it possible to handle such situations. For example, text values could be grouped based on their first letters, while URIs could be grouped based on a common pattern. Such views would be rated low, but would act as fallbacks when no other view is available.

Discussion and Future Work

Follow-your-nose style navigation on the Web of Data can be roughly compared to how users browse pages on the classic Web: they follow hyperlinks. This works well in open worlds of linked documents or linked data, because following a link is basically a question of dereferencing what is on the other side of that link. The process just gets repeated again and again, exploring one path at a time. Things are not that simple when considering set-based navigation and semantic paths, as we do in S-Paths. We want to browse many resources simultaneously and look beyond the direct properties of those resources, following longer paths that lead to relevant information about them. This raises multiple practical questions. What sets of resources do we expose to bootstrap the exploration process? How deep down the paths do we go? Do we consider all possible paths? How many interlinked graphs do we traverse? Contrary to followyour-nose navigation, considering (even theoretically) the open world in its entirety is not an option. Answering the previous questions necessarily entails delimiting perimeters in the data, that both the system and its users will be able to cope with. S-Paths takes named graphs as the unit to delimit such perimeters. At first, this might seem contradictory with the very notion of a Web of Data, the whole point being to break out of data silos by having direct links between resources in different graphs from different datasets, and enabling the easy traversal of those links. Our purpose, however, is not to re-introduce artificial silos. It is rather to have some means to group sets of resources meaningfully, and to identify coherent ensembles of semantic paths describing those resources. Small combinations of named graphs seem to be reasonable candidates to act as perimeters for such a purpose.

For now, S-Paths supports this approach by having the system connect to a single, local SPARQL endpoint that hosts one or more RDF graphs. For instance, the simple Nobel prize example used throughout the paper makes use of two linked graphs: the Nobel prize dataset itself, and an extract from DBpedia with the names and geo-coordinates of places, as well as pictures of people. While these two graphs are hosted behind the same SPARQL endpoint, we could imagine explore graphs in distant endpoints using the SPARQL SERVICE clause.

However, this would come with significant performance issues, and would not be sufficient to enable users to navigate seamlessly across numerous linked graphs. Right now, graphs to include in the perimeter have to be declared manually. As we do not want to have all graphs merged into one huge perimeter (which would defeat the whole point of defining a perimeter and would be practically impossible anyway), we need S-Paths to be capable of dynamically redefining its perimeter in a way that is transparent to users: seamlessly adding new datasets to it based on the semantic paths followed, discarding datasets that are no longer relevant.

This also requires determining the best way to dynamically update the semantic path characterizations that S-Paths relies upon to rank and configure views. These characterizations need to be updated whenever the data change. But S-Paths cannot easily know when data hosted at remote endpoints change. Theoretically, the system is able to perform this analysis on the fly, since users can start browsing as soon as S-Paths has retrieved the first few paths, which only takes a few seconds. But having S-Paths permanently scan graphs is neither reasonable nor scalable. The characterizations also need to be updated when the perimeter changes, i.e., when graphs are added or removed. Knowing that a full analysis requires from several minutes to several hours depending on the number, size and structure of the graphs considered, an interesting hybrid approach would be to have data providers pub-lish characterizations alongside their graphs (these are relatively small and simple JSON files). S-Paths would then only need to analyze connections between graphs when the perimeter changes. Achieving this would turn S-Paths into a full-fledged linked data browser combining set-based and follow-your-nose style navigation into a single tool.

Further evaluation will be needed. A key finding is that S-Paths lets users memorize the outlines of a dataset. It would be interesting to compare it with other Linked Data browsers in this respect. Another axis could be to try to understand which aspect of S-Paths supports memorizing. This is an intricate question since it is a complex system, and we had to combine a number strategies to make browsing sets of entities even possible. Another promising result is that S-Paths can support users in finding ideas to reuse data. This is a crucial point for adoption of Linked Data, and as for memorizing, it would be worth investigating which aspects of the tool makes it possible.

Finally, we designed S-Paths to support the discovery of unknown datasets, but if we mean to turn it into an exploratory search browser, we also need to evaluate its performance when users know what they are looking for, and when they switch from open exploration to focused search, and the other way round.

Fig. 2 .

 2 Fig.2. Query templates dividing the query in Figure1into multiple queries. The first query is called iteratively for each path of depth n, to find all the paths of depth n + 1 extending this path. The second and third queries are called for each path.

Fig. 3 .

 3 Fig. 3. 2D density plot view definition.

Fig. 4 .

 4 Fig. 4. Query templates used to populate views.

Fig. 5 .

 5 Fig. 5. Process for generating a default view.

Fig. 6 .

 6 Fig. 6. (a) Default view on Laureates, showing their date of birth (one-step semantic path dateOfBirth mapped to x-axis) and their gender (one-step semantic path gender mapped to color scale). (b) Switching dimensions to award year (two-step semantic path award/year aggregated by decade) and discipline (three-step semantic path laureateAward/category/label mapped to color scale). (c) Switching to a map view offers as first choice the laureates' birthplace latitude and longitude as the dimensions used to plot Nobel laureates on the map (three-step semantic path dbpedia:birthPlace/owl:sameAs/wgs84_pos:lat and wgs84_pos:long). It is possible to switch to the dbpedia:deathPlace.

Fig. 7 .

 7 Fig. 7. Animated transition from a sub-selection made in a 2D density plot showing counts for types of Award File aggregated by decade (1), to a histogram showing the distribution of prizes per discipline for each individual year (5). Sample intermediate frames: (2) elements no longer present in the target view are faded out, and visual marks corresponding to aggregates get decomposed into groups that will transition towards the same target; (3-4) elements present in both the source and target views get smoothly interpolated along relevant encoding channels: position, color, shape; (5) elements that did not exist in the source view fade in.

Fig. 8 .

 8 Fig. 8. Brushing & Linking between two views: items selected on the map are highlighted in the histogram.

Fig. 9 .

 9 Fig. 9. Key views illustrating the Nobel prize use case: (a) 2D density plot showing the count of awards per year (binned by decade) and category; (b) showing award shares instead of years; (c) histogram showing the repartition of awards by gender over the years; (d) map showing the birthplace of award laureates; now considering laureates as the resource set: (e) histogram showing laureates' gender and birth year; (f) info card detailing all semantic paths for one laureate in the set; (g) histogram showing gender balance by award category; (h) timeline of events in the life of a subset of laureates.

  ∃ e ∈ E, ∃ o ∈ O ⊂ {U∪L}, (e p 1 /p 2 / . . . /p n o)

	Characteristic	Description
	entrypoint	rdf:type shared by the resources
		one of: datetime, geographical
	category	coordinate, image, number, text or
		URI
	depth	number of statements from the set of entities to the set of values
	coverage	percentage of entities in the set for which this path actually exists
	count	total number of values (or URIs) at the end of the path
	unique count	number of unique values (or URIs) at the end of the path
		Table 1
	Characteristics of semantic paths.
		(e 1 rdf:type C) and (e 2 rdf:type C)
		a semantic path is a set of objects O related to the set of
		resources E by a sequence of properties p 1 , p 2 , . . . , p n ,
		with n 1, such that:

  Fig.1. Conceptual query template to retrieve paths characteristics for all paths of depth n. S-Paths splits this query into multiple queries, following a divide-and-conquer strategy, as described in Figure2.

	1 SELECT DISTINCT 2 ?p1 ?p2 ?pn	path of depth n
	3	(COUNT(DISTINCT ?values) as ?uniqueValues)
	4 5	(COUNT(DISTINCT ?entities) as ?nbCoveredEntities) (COUNT(?values) as ?totalValues)	coverage and count
	6 7	?datatype ?isiri ?isliteral ?language (AVG(?charlength) as ?avgcharlength)	category
	8 WHERE {
	9	?entities rdf:type <TYPE_URI> .
	10	?entities ?p1 ?o1 . ?o1 ?p2 ?o2 . ?o2 ?pn ?values .
	11	FILTER (?entities != ?o1 &&
	12	?entities != ?o2 &&
	13 14	?entities != ?values && ?o1!= ?values &&	prevent from looping
	15	?o2!= ?values &&
	16	?o1!= ?o2
	17	) .
	18	BIND(datatype(?values) as ?datatype)
	19	BIND(ISIRI(?values) AS ?isiri) .
	20	BIND(ISLITERAL(?values) AS ?isliteral) .
	21	BIND(LANG(?values) AS ?language) .
	22	BIND(STRLEN(xsd:string(?values)) AS ?charlength) .
	23 }
	24 GROUP BY ?p1 ?p2 ?p3 ?datatype ?isiri ?isliteral ?language
	QUERY TEMPLATE TO RETRIEVE PATHS EXTENDING A PATH
	1 SELECT DISTINCT ?property WHERE {
	2 3	?entities rdf:type <TYPE_URI> . ?entities ?p1 ?o1 . ?o1 ?p2 ?o2 . ?o2 ?pn ?on .	given path
	4	?on ?property ?values .	extensions n + 1
	5	FILTER (?entities != ?o1 &&
	6	?entities != ?o2 &&
	7	?entities != ?on &&
	8 9	?o1!= ?on && ?o2!= ?on &&	prevent from looping
	10	?o1!= ?o2
	11	) .
	12 }
	QUERY TEMPLATE TO RETRIEVE COVERAGE AND COUNT FOR A PATH
	13 SELECT
	14	(COUNT(DISTINCT ?values) AS ?unique)
	15 16	(COUNT(?values) AS ?total) (COUNT(DISTINCT ?entities) AS ?nbCoveredEntities)	coverage and count
	17 WHERE {
	18 19	?entities rdf:type <TYPE_URI> . ?entities ?p1 ?o1 . ?o1 ?p2 ?o2 . ?o2 ?pn ?values .	given path
	20	FILTER (?entities != ?o1 &&
	21	?entities != ?o2 &&
	22 23	?entities != ?values && ?o1!= ?values &&	prevent from looping
	24	?o2!= ?values &&
	25	?o1!= ?o2
	26	) .
	27 }
	QUERY TEMPLATE TO RETRIEVE CATEGORY FOR A PATH
	28 SELECT DISTINCT
	29 30	?datatype ?isiri ?isliteral ?language (AVG(?charlength) as ?avgcharlength)	category
	31 WHERE {
	32 33	?entities rdf:type <TYPE_URI> . ?entities ?p1 ?o1 . ?o1 ?p2 ?o2 . ?o2 ?pn ?values .	given path
	34	FILTER (?entities != ?o1 &&
	35	?entities != ?o2 &&
	36 37	?entities != ?values && ?o1!= ?values &&	prevent from looping
	38	?o2!= ?values &&
	39	?o1!= ?o2
	40	) .
	41	BIND(datatype(?values) as ?datatype)
	42	BIND(ISIRI(?values) AS ?isiri) .
	43	BIND(ISLITERAL(?values) AS ?isliteral) .
	44	BIND(LANG(?values) AS ?language) .
	45	BIND(STRLEN(xsd:string(?values)) AS ?charlength) .
	46 }
	47 GROUP BY ?datatype ?isiri ?isliteral ?language

Table 2 Default

 2

	View	Type	Weight	Number of resources	dimension 1	dimension 2	dimension 3
	density plot	aggregate	0.5		datetime, text or uri	text or uri
	treemap	aggregate	0.3		single path: text or uri
	stacked chart	multiple distinct	0.9	min/max: [2, 1000] optimal: [4, 200]	single path: datetime, text or uri	single path: text or uri
	timeline	multiple distinct	0.85	min/max: [2, 50] optimal: [10, 20]	all datetime paths	single path: text or uri
	URI wheel	multiple distinct	0.4	min: 2	uri
	map	multiple distinct	0.85	min/max: [2,1000]	geo	geo	text
	breakdown by values	multiple distinct	0.7	max: 50, optimal: [1, 30]	single path: any category
	images	multiple distinct	0.8	min/max: [2, 1000]	single path: image	single path: text
	info card	single entity	1	min/max: [1,1]	all paths
	node link diagram	single entity	0.5	min/max: [1,1]	all paths

configuration of view templates as configured for the Nobel dataset.

http://data.nobelprize.org

https://gitlab.inria.fr/mdestand/s-paths

http://s-paths.lri.fr

Indicative tasks for lay users are in Appendix A.

Questions for lay users and reusers are in Appendix B.

http://legilux.public.lu/

http://www.nobelprize.org/about/linked-data-examples/

http://api.bnf.fr/ (we ran our test on a 10 percent sample.)

http://data.public.lu/fr/datasets/legilux-journal-officiel-dugrand-duche-de-luxembourg/

[START_REF] Schraefel | The Pathetic Fallacy of RDF[END_REF] https://old.datahub.io/dataset/

rism[START_REF] Camarda | Exploring the Web of Data[END_REF] http://raimond.me.uk/resources/peel

.tar.gz 12 https://bitbucket.org/biktorrr/amlod/

downloads/ 13 https://old.datahub.io/dataset/linkedmdb


Dr Edouard Girard
email: edouard.girard@univ-grenoble-alpes.fr

Grégory Chagnon

Alexandre Moreau-Gaudry

Christian Letoublon

Denis Favier

Stéphane Dejean

Bertrand Trilling

Benjamin Nottelet
email: benjamin.nottelet@umontpellier.fr

Benjamin Pr

Nottelet

Evaluation of a biodegradable PLA-PEG-PLA internal biliary stent for liver transplantation: in vitro degradation and mechanical properties

Keywords: Liver transplantation, Biliary Fistula, Internal Biliary Stenting, Absorbable Implants, Polylactide-Polyethylene glycol coplymers, Mechanical properties

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

INTRODUCTION

Biliary complications in Liver Transplantation (LT) are a significant source of postoperative morbidity and mortality, induce a severe financial burden and may eventually compromise outcomes [START_REF] Welling | Biliary complications following liver transplantation in the model for end-stage liver disease era: Effect of donor, recipient, and technical factors[END_REF]- [START_REF] Akamatsu | Biliary reconstruction, its complications and management of biliary complications after adult liver transplantation: a systematic review of the incidence, risk factors and outcome[END_REF] . Complications arising from the biliary anastomosis (leakage, stricture) are usually considered as the technical Achilles heel of LT. In the literature, incidence of anastomotic biliary complications remains high, ranging from 10% to 50% [START_REF] Goumard | Biliary reconstruction with or without an intraductal removable stent in liver transplantation: study protocol for a randomized controlled trial[END_REF] . Duct-to-duct reconstruction with an external stent implantation (T-tube) has been the gold standard for many years, however, and although the debate is still open, a growing number of centers have abandoned T-tube placement due to evidences pointing out at specific T-tube induced morbidity ( 5)- (10) . Instead, the use of internal biliary stenting (IBS) has been reported as a safe alternative allowing to decrease anastomotic biliary complications [START_REF] Girard | Internal biliary stenting in liver transplantation[END_REF]- [START_REF] Barkun | Do biliary endoprostheses decrease biliary complications after liver transplantation?[END_REF] . Although IBS is an interesting option, several technical issues such as the nature of the material (silicone, rubber) require further refinement. In particular, the main disadvantage of the materials currently used is their non-degradability, which leads to an additional surgical procedure for ablation, involving potential complications and an additional cost. For this reason, ideally duct-to-duct reconstruction should be performed with intraoperative insertion of a Resorbable Internal Biliary Stent (RIBS).

To be usable and useful, such RIBS must comply with many specifications (biocompatibility, appropriate mechanical properties etc.). In particular, based on incidence of anastomotic biliary leakage and anastomotic biliary stricture in literature [START_REF] Kochhar | Biliary complications following liver transplantation[END_REF], [START_REF] Nemes | Biliary complications after liver transplantation[END_REF] , RIBS must be impermeable for a minimum of 4 weeks to prevent bile leak and it must calibrate the anastomosis for 8 weeks to avoid bile duct strictures, and it must be completely degraded within 6 months without release of macroparticles. In this context, biodegradable aliphatic polyesters, including polyglycolide (PGA), polylactide (PLA), and their copolymers (PLGA) are materials of choice and were used for fabrication of resorbable implantable medical devices and scaffolds for tissue engineering (17)- (21) . Despite of biodegradable stent development in clinical practice for diverse applications, especially vascular [START_REF] Rogacka | Bioabsorbable and biocompatible stents. Is a new revolution coming?[END_REF], [START_REF] Brown | A New Wave in Treatment of Vascular Occlusive Disease: Biodegradable Stents-Clinical Experience and Scientific Principles[END_REF] , only a limited number of studies was realized for biliary system. Xu et al in 2009 investigated degradation of a biodegradable poly(L-lactide-co-glycolide) (PLGA) stent in vitro in bile [START_REF] Xu | Feasibility of biodegradable PLGA common bile duct stents: an in vitro and in vivo study[END_REF] . Physicochemical and mechanical characteristics were compatible with bile duct implantation, but material complete degradation duration was about 4 or 5 weeks, which is not long enough for a LT application. In parallel, PLGA stent degradation in large animals' bile ducts (dog or pig) has been evaluated, which demonstrated good biocompatibility and no bile sludge stent obstruction [START_REF] Xu | Feasibility of biodegradable PLGA common bile duct stents: an in vitro and in vivo study[END_REF]- [START_REF] Laukkarinen | A novel biodegradable biliary stent in the endoscopic treatment of cystic-duct leakage after cholecystectomy[END_REF] . In another approach, Tashiro et al. evaluated the use of a poly(L-lactide-co--caprolactone) (L-LA/CL 50:50) biliary stent on a porcine transplant model, and validated a resorption without biliary leak or obstructive cholestasis [START_REF] Tashiro | Synthetic bioabsorbable stent material for duct-to-duct biliary reconstruction[END_REF] . Most of the proposed materials suffers however from either a fast degradation under bile duct conditions, or inadequate mechanical properties (initially to weak or too rigid). These examples illustrate the prime importance of combined kinetics of degradation and mechanical properties for the material selection. In this frame, tremendous amounts of recent research have therefore focused on the use of PLA/poly(ether) copolymers to modulate these properties for applications ranging from vascular grafts, to nerve guides or bone scaffolds [START_REF] Tara | Well-organized neointima of large-pore poly(L-lactic acid) vascular graft coated with poly(L-lactic-co-εcaprolactone) prevents calcific deposition compared to small-pore electrospun poly(L-lactic acid) graft in a mouse aortic implantation model[END_REF]- [START_REF] Bhaskar | Composite porous scaffold of PEG/PLA support improved bone matrix deposition in vitro compared to PLA-only scaffolds[END_REF] . In particular, some of us demonstrated that PLA-Poloxamer and PLA-Poloxamine triblock copolymers can be good candidates for ligament tissue engineering as, besides ease of processability, their mechanical and degradation properties can be easily tuned to meet the application requirements [START_REF] Leroy | Investigation on the properties of linear PLA-poloxamer and star PLA-poloxamine copolymers for temporary biomedical applications[END_REF]- [START_REF] Pinese | In vivo evaluation of hybrid patches composed of PLA based copolymers and collagen/chondroitin sulfate for ligament tissue regeneration: Hybrid Patches for Ligament Reconstruction[END_REF] . In an effort to produce degradable copolymers matching the mechanical properties of softer tissues, we also investigated another family of poly(lactide)-b-poly(ethylene glycol)-bpoly(lactide) (PLA-b-PEG-b-PLA) by focusing on the modelling of their mechanical behavior over degradation that was fitted with a non-linear viscoelastic model [START_REF] Breche | Mechanical behaviour׳s evolution of a PLA-b-PEG-b-PLA triblock copolymer during hydrolytic degradation[END_REF], [START_REF] Breche | A non-linear viscoelastic model to describe the mechanical behavior's evolution of biodegradable polymers during hydrolytic degradation[END_REF] .

Taking advantage of their properties the aim of the present work is therefore to design a RIBS based on a selected PLA-b-PEG-b-PLA to secure biliary anastomose during healing and avoid complications such as bile leak and stricture. In more details, the objectives are to evaluate the mechanical properties of a RIBS prototype with respect to the common bile duct stenting requirements in liver transplantation. For this purpose, the mechanical properties and the permeability are evaluated over degradation under simulated biliary conditions to explore the usefulness of a PLA-b-PEG-b-PLA RIBS to secure biliary anastomosis.

MATERIALS AND METHODS

2.1.Material

Chemicals were provided by Sigma-Aldrich (Saint-Quentin-Fallavier, France). Phosphatebuffered saline (PBS) was purchased from Invitrogen (Cergy-Pontoise, France). D,L-lactide (D,L-LA) was purchased from Purac (Lyon, France). Solvents and chemicals were used without any further purification. Silicone stent was purchased from Péters Surgical (Bobigny, France). [START_REF] Welling | Biliary complications following liver transplantation in the model for end-stage liver disease era: Effect of donor, recipient, and technical factors[END_REF] H NMR spectra were recorded with a 300MHz AMX300 Bruker spectrometer at room temperature. Solvent used was deuterated chloroform, chemical shifts were indicated in ppm with tetramethylsilane (TMS) as a reference.

2.2.Physicochemical characterization

Number average molecular weight (Mn) and dispersity (Ð) were obtained by Size Exclusion Chromatography (SEC) with a Viscotek GPCMax auto sampler system fitted two Viscotek LT5000L Mixed Medium columns (300 mm x 7.8 mm), a Viscotek VE 3580 RI detector. The mobile phase was tetrahydrofuran (THF) at 1 mL/min flow and 30°C. The polymer was dissolved in THF to reach 10 mg/mL solution that was filtered through a 0.45 μm Millipore filter before injection. Mn was expressed according to polystyrene standards calibration.

2.3.Copolymers synthesis and RIBS prototype manufacturing

Triblock copolymer of PLA-b-PEG-b-PLA was realized following a previously described procedure [START_REF] Leroy | Investigation on the properties of linear PLA-poloxamer and star PLA-poloxamine copolymers for temporary biomedical applications[END_REF] . In a typical synthesis, predetermined amounts of D,L-LA and PEG were introduced in a round-bottom flask. The catalyst Sn(Oct)2 was then added (0.1molar % with respect to LA units). After degassing, and sealing of the flask under vacuum, the polymerization was allowed to proceed at 110°C for 5 days. The copolymer was then recovered by dissolution in dichloromethane (DCM), precipitation in cold diethyl ether, and drying under reduced pressure to constant mass. The copolymer was obtained with a yield of 90%. Polymerization Degree (DP) of each PLA block is defined as:

(1) 𝐷𝑃 𝑃𝐿𝐴 (%) = with EG/LA being the ratio of ethylene oxide and lactyl units calculated from 1 H NMR spectra, [START_REF] Welling | Biliary complications following liver transplantation in the model for end-stage liver disease era: Effect of donor, recipient, and technical factors[END_REF] H NMR: (300MHz; CDCl3): δ (ppm)=5.1 (q, 1H, CO-CH(CH3)-O), 3.6 (s, 4H, CH2-CH2-O), 1.5 (m, 3H, CO-CH(CH3)-O). Mntribloc=345 000 g/mol, LA/EG=10/1.

The molecular weight of the achieved triblock copolymers is determined as:

(2) 𝑀 𝑛𝑡𝑟𝑖𝑏𝑙𝑜𝑐 (%) = 2 × (𝐷𝑃 𝑃𝐿𝐴 × 72) + 𝑀 𝑛𝑃𝐸𝐺 with MnPEG = 20 000 g/mol.

Polymer films with a targeted thickness of 0.6 mm (based on commercially available stents) were realized by solvent evaporation. A predetermined polymer quantity was solubilized in acetone, the solution was poured in a small plate and evaporation was realized for 36h under an extractor hood. Final solvent removal was produced by further drying in vacuum under 1.10 -3 mbar for 3 days. A 0.5 mm thick film was produced.

RIBS was then fabricated by film-rolling and gluing by means of a partial dissolution of the polymer film surface. A 45 mm x 1.5 mm rectangular plate was cut from the film and then wound around a metallic stent with 4.6 mm external diameter. The gluing was achieved using acetone. RIBS dimensions were: external diameter 5.6 mm, internal diameter 4.6 mm, length 45 mm, an illustration is presented in Figure 1.

2.4.In vitro degradation studies

PLA-b-PEG-b-PLA hydrolytic degradation was investigated under physiological conditions at 37 °C, under stirring 100 rpm, and protected from light. In more details, a "control group" was degraded under classical conditions, ie in PBS (pH 7.2) while a "biliary group" was degraded in a simulated bile fluid reproducing bile composition and pH (pH 8.4). Biliary pH physiologically oscillates between 7 and 8.4. To increase probability of finding difference, if any, the most basic pH was chosen, which corresponds to the worst case scenario in terms of degradation kinetics. This simulated bile fluid was made according to a Sörensen model by mixing 96.5 mL of Na2HPO4 133 mmol/L (23.67 g Na2HPO4 per liter of water) with 3.5 mL of KH2PO4 133 mmol/L (18.10 g of KH2PO4 per liter of water) to 100 mL of solution. The pH of solutions was tested weekly, and solutions were replaced when it fell below a threshold value (pH <7 for the control group and pH <8 for biliary group).

Measurements at predefined degradation time points were performed in triplicate and expressed as mean values ± SD.

For mass loss measurement, RIBS were placed in 20 mL test stents and submitted to 12 weeks of degradation the selected fluid (PBS or 'biliary' fluid according to the group) at 37°C within an agitator/incubator. The initial mass (m0) was measured and correspond to the mass of the sample priori to degradation. At given time-points, films were taken out of the solution, weighted, dried and weighted again to obtain the hydrated mass (mhyd) and the dry mass (md).

Mass loss and water uptake were then calculated according to:

(3) Mass loss (%) = 𝑚 0 -𝑚 𝑑 𝑚 0 × 100 (4) Water uptake (%) = 𝑚 ℎ𝑦𝑑 -𝑚 0 𝑚 0 × 100
Finally, in addition to molecular weight and mass loss measurements, macroscopic RIBS observation were made at each degradation time from a surgical point of view by a trained surgeon. Degradation solutions were filtered with a 0.45 m pore size and 47 mm diameter cellulose acetate membrane filter. The membrane filter was then analyzed by microscopy imaging (x40 magnification) to measure the size of particles that may were retained.

2.5.Permeability test

Samples used were 0.5 mm thick and 25 mm diameter circular polymer films. Permeability of samples was tested using a horizontal diffusion chamber as presented in Figure 2. Two 5 mL glass compartments were separated by the film to be tested. Seal was made by apposition of a cellulose joint on either side of the polymer film. First chamber was filled with degradation solution, which was maintained at 37 °C. A water column of 20.3 cm was disposed on the first chamber in order to exert on the plate a 15 mmHg pressure (simulating internal pressure of bile duct). Pressure of 15 mmHg was maintained 24 hours on the plate. To assess porosity, amount of liquid in the second chamber was measured.

2.6.Mechanical properties measurement

RIBS samples were put in degradation medium following the protocol described in paragraph For comparison, the same mechanical test was applied on a silicone stent (Tubular drain  -Péters Surgical, external diameter 5.3 mm, internal diameter 4.8 mm, length segment 5 mm) currently used in liver transplantation [START_REF] Girard | Internal biliary stenting in liver transplantation[END_REF] .

RESULTS

3.1.Syntheses

In a preliminary study, we synthesized multiblock copolymers made of amorphous PLA50 (also known as PD,L-LA) and Pluronic®, Poloxamer® or PEG by ring-opening polymerization of lactide (Table 1). Based on preliminary evaluation and previous studies (resumed on Table 1), PLA50-b-PEG-b-PLA50 was selected by a trained surgeon for RIBS development as it showed mechanical and degradation properties corresponding to specifications, assessing material for implantation.

Molecular weights of the copolymers were firstly determined by 1 H NMR spectroscopy, by means of Eqs. ( 1) and (2). Mntribloc was 345 000 g/mol. Results were close to theoretical values mentioned in methods section, although a little higher. On the opposite, SEC analyses gave molecular weight values about two times lower than those calculated by NMR, with an average Mntribloc at 179 000 g/mol. This difference was explained by the use of polystyrene standards for SEC calibration causing inaccurate measurements with aliphatic polyesters [START_REF] Kowalski | Polymerization of L , L -Lactide Initiated by Aluminum Isopropoxide Trimer or Tetramer[END_REF], [START_REF] Huang | Synthesis and degradation of PLA-PCL-PLA triblock copolymer prepared by successive polymerization of ε-caprolactone and dl-lactide[END_REF] . The amphiphilicity of the triblock copolymers, although limited by the low content of PEG, leads to modified hydrodynamic volumes, increased retention times, and results in underestimated values.

3.2.In vitro degradation

Morphological change

From a macroscopically point of view, during the degradation period, RIBS color gradually changed from an initial translucent state to a whitish color during the first week, and turned opaque white from the second week. From a surgical qualitative point of view, although initially relatively flexible before the degradation, the material gradually became stiffer until the 3 rd week, before becoming fragile and brittle from the 6 th week. After 8th week, still brittle, it became slightly deformable. Its shape and integrity could not be fully maintained from the 12th week, evolving to a friable and labile consistency, making tests impossible.

The degradation medium was filtered to track the presence of small polymer particles leaching out of the stent bulk upon degradation. No particles were identified on the filters under optical microscope observation at ×40 magnification.

Mass loss, water uptake and molecular weight

The mass loss and the water uptake are presented in Figure 3 with an exponential function being observed for the polymer water uptake over time. Water uptake was 25% at 2 weeks, 50% at 4 weeks, 100% at 6 weeks, reaching more than 1000% at 12 weeks. Two distinctive periods are visible. During the three first weeks, the mass loss rate was lower (about 3% per week) compared to the following weeks (about 10% per week). After this period, molecular weight decrease was quasi linear. After the 12th week, even if polymers were not fully degraded, weight loss measurements were impossible to perform because of their friable consistency. Unlike mass loss, the molecular weight decrease was very important during the two first weeks as illustrated in Figure 4 with a 60% decrease. Dispersity index presented in Figure 4 is defined as the ratio of the mass average molecular weight and the number average molecular weight and describes the distribution of molecular mass in a given polymer sample.

As expected, the increase of dispersity index follows the decrease of molecular weight. Over the degradation period studied, no significant differences were observed for mass loss, the water uptake and weight loss for the "control group" (pH 7.2) and the "biliary group" (pH 8.4).

Permeability evolution

The material was impermeable until the 8th week of in vitro degradation. There was no fluid diffusion from 1st to 2nd chamber, for both groups (control group and biliary group). From the 10th week, the tests were not practicable because of the fragility of the material at this stage of degradation.

Influence of pH variations

Based on the reported degradation results for RIBS, no significant difference was identified between the two experimental groups. Whether for mass loss, water uptake or molecular weight, as well as for permeability or mechanical behavior.

3.3.Mechanical properties evolution

Figure 5A presents a typical result of a compression test on a RIBS, the illustration is proposed for 1 degradation week. All curves have the same general appearance. Each deformation cycle was characterized by a load (10, 20 or 50%) followed by an unload to zero stress. There was a strength plateau above a strain of 10% and stiffening after a strain of 30%. Unload could be decomposed into two phases: an instantaneous relaxation corresponding strength fall for a constant strain, and a return to zero stress. Regardless of degradation time, the return phase was constant for all samples, systematically starting at 1 N force (end of the instantaneous relaxation). The residual strain was 8% for 10% strain load, 15% for 20% strain load, and 40%

for 50% strain load. For very large displacements, a strain hardening can be observed meaning that the closures of the RIBS would need a large amount of force. Result of the same mechanical test applied on a silicone stent is presented in Figure 5B. The curve presents a similar level of force for similar deformation, the main difference is that the initial slope is greater for the PLAb-PEG-b-PLA and that the material presents more hysteresis.

The PLA-b-PEG-b-PLA curve evolves with the degradation process. The slopes of curves (represented by red arrows on Figure 4A) was evaluated for each deformation cycle at 10, 20 and 50% and measured for each degradation time. The results are presented in Figure 6. It appears that the stiffness of the RIBS is first increasing during three weeks and is then continuously decreasing until 10 weeks.

To measure the influence of the hysteresis of the material, the evolution of the work necessary to load and unload the material at 10, 20 and 50% was calculated, the result is presented in Figure 7. As for the stiffness, the amount of work becomes greater after some weeks before drastically decreasing, illustrating the loss of mechanical properties. Work curves decrease was more important than the stiffness one.

DISCUSSION

In an attempt to provide an alternative to RIBS that have poor mechanical properties or inadequate degradation (too slow for PCL or crystalline PLA, too fast for PLGA), we synthesized in a preliminary study multiblock copolymers made of amorphous PLA50 and Pluronic®, Poloxamer® or PEG (Table 1). In a previous study, we reported that this strategy allows to finely control the properties of the obtained copolymers such as their crystallinity, glass transition temperature, degradation kinetics [START_REF] Leroy | Investigation on the properties of linear PLA-poloxamer and star PLA-poloxamine copolymers for temporary biomedical applications[END_REF] . This makes it possible to find the best match between the requirements of an application and suitable copolymers. Based on preliminary evaluation and previous studies (resumed on Table 1), PLA50-b-PEG-b-PLA50 was selected by a trained surgeon for RIBS development as it showed mechanical and degradation properties corresponding to specifications, assessing material for implantation (flexibility after drying, low Young's modulus and in vivo estimated degradation time of about 6 months for a complete resorption). The aim of the present work was to design a PLA-b-PEG-b-PLA RIBS to secure biliary anastomose during healing and avoid complications such as bile leak and stricture. We evaluated the mechanical properties of a RIBS prototype with respect to the common bile duct stenting requirements in liver transplantation. For this purpose, the mechanical properties and the permeability are evaluated over degradation under simulated biliary conditions to explore the usefulness of a PLA-b-PEG-b-PLA RIBS to secure biliary anastomosis. Of notice, we chose to only take pH into account in our simulated biliary conditions but not viscosity. Viscosity is an important parameter of bile that changes as a function of the flow. However, it has been reported that for the 65% of patients the viscosity of bile under flow from the common bile duct is between water viscosity (0.7 mPa.s) and the lower limit of plasma viscosity (1.1 mPa.s), and that cholecystectomized patients (as in transplant) had a lower bile viscosity [START_REF] Reinhart | Viscosity of human bile sampled from the common bile duct[END_REF], [START_REF] Mcmaster | Bile studies after liver transplantation[END_REF] . Bile viscosities did not differ according to pathologies (choledocholithiasis, cholangitis, biliary pancreatitis, carcinoma, or transplant). Our study being centered on the in vitro degradation characteristics in a static context with aqueous buffers, the viscosity has therefore not been further considered.

Regarding morphological change, color change is due to the presence of water domains in the polymer matrix whose size and number affects the whitening effect that increases with immersion/degradation time [START_REF] Jiang | Water whitening of polymer films: Mechanistic studies and comparisons between water and solvent borne films[END_REF] .

In order to evaluate the risk of bile duct obstruction the degradation medium was filtered to track the presence of small polymer particles leaching out of the stent bulk upon degradation.

The Oddi sphincter size is about a millimeter. There was thus no production of millimeter particles during degradation that could potentially be responsible for a biliary obstacle.

The mass loss gave information about water soluble oligomers generated during the hydrolysis process and released out of the polymer bulk. Two distinctive periods are visible. During the three first weeks, the mass loss rate was lower compared to the following weeks. This induction period is commonly observed during the degradation of aliphatic polyesters and is due to the difficulty, at first, for the degraded chains to diffuse out of the sample [START_REF] Leroy | Investigation on the properties of linear PLA-poloxamer and star PLA-poloxamine copolymers for temporary biomedical applications[END_REF], [START_REF] Li | Structure-property relationships in the case of the degradation of massive aliphatic poly-(α-hydroxy acids) in aqueous media[END_REF] . After this period, the lower molecular weight and therefore lower entanglement allow the leaching of the degradation products in the degradation medium, which leads to a quasi-linear weight decrease.

Unlike mass loss, the molecular weight decrease was very important during the two first weeks.

This trend is explained by the highest concentration of ester bonds per volume unit leading to a greater ability of long chains to be hydrolyzed [START_REF] Wang | A phenomenological model for the degradation of biodegradable polymers[END_REF] . In final steps, probability of scission and hydrolysis ratio practically doesn't exist because of very low ester bonds concentration. As expected, the increase of dispersity index follows the decrease of molecular weight. These results highlight the rise of dispersion of chain lengths due to the random scissions of polymer chains that occur during the degradation process. After the 12th week, even if polymers were not fully degraded, weight loss measurements were impossible to perform because of their friable consistency. Polyester-polyether block copolymers degradation is known to proceed via a bulk erosion, with random polymer chains scissions. The chains became progressively shorter during degradation, releasing soluble oligomers in the media. While keeping its original shape, polymer sample became therefore more brittle.

The material was impermeable until the 8th week of in vitro degradation. Based on incidence of anastomotic biliary leakage in literature [START_REF] Kochhar | Biliary complications following liver transplantation[END_REF],( 15), [START_REF] Nemes | Biliary complications after liver transplantation[END_REF] , to prevent bile leak, RIBS must be impermeable for a minimum of 4 weeks. Specifications were respected on this point.

Based on the reported degradation results for RIBS, no significant difference was identified between the two experimental groups. The pH difference between the 2 study groups (i.e.

"control group" with a 7.2 pH solution vs "biliary group" with an 8.4 pH solution) was too small to induce basic catalysis in biliary group. These results are confirmed by literature data, for acid or basic catalysis, pH differences must be higher, respectively less than 3 or more than 10 ( 46), [START_REF] Tsuji | Properties and morphology of poly(L-lactide). II. hydrolysis in alkaline solution[END_REF] . Physiological bile pH variations are between 7 and 8.4 [START_REF] Esteller | Physiology of bile secretion[END_REF] . As a result, these biliary pH variations have no impact on RIBS degradation kinetics, the selected PLA-b-PEG-b-PLA copolymer can stand the more alkaline conditions found in the common bile duct.

The mechanical comparison between silicone stent and RIBS is not obvious. The curve presents a similar level of force for similar deformation, the main difference is that the initial slope is greater for the PLA-b-PEG-b-PLA and that the material presents more hysteresis. The silicone stent is efficient to solve the clinical problem but not perfect, the PLA-b-PEG-b-PLA having closed stiffness must be also a good candidate, but with different mechanical properties as hysteresis and the stress plateau. The observed evolution of RIBS stiffness, but also color changes can be explained as follows. It appears that the stiffness of the RIBS is first increasing during three weeks due to microphase separation in copolymers and is then continuously decreasing until 10 weeks, illustrating the normal degradation process. In triblock copolymer PLA-b-PEG-b-PLA, PEG short blocks have a role of plasticizer and chains mobility and phase separation are facilitated by the water uptake that plasticizes the polymer. In the case of PLAb-PEG-b-PLA, this water uptake leads to micro-phase separation of the PLA and PEG blocks, which results in the fact that the plasticization of long PLA blocks by the short PEG blocks (more flexible with lower transition temperature) loses its effectiveness at the beginning of degradation [START_REF] Kissel | ABA-triblock copolymers from biodegradable polyester A-blocks and hydrophilic poly(ethylene oxide) B-blocks as a candidate for in situ forming hydrogel delivery systems for proteins[END_REF], [START_REF] Lu | Synthesis and characterization of a series of biodegradable and biocompatible PEG-supported poly(lactic-ran-glycolic acid) amphiphilic barbell-like copolymers[END_REF] . Evolution of polymer properties during the first 3 weeks can therefore be explained by 2 phenomena. First, water uptake causes material whitening and a little plasticization [START_REF] Jiang | Water whitening of polymer films: Mechanistic studies and comparisons between water and solvent borne films[END_REF] . In the present case, this plasticization effect is not perceptible because it is associated with the second phenomenon of micro-phase separation. This phenomenon in the triblock copolymers, results in a loss of plasticization of the PLA long blocks by the PEG short blocks, and in a stiffening of the structure [START_REF] Lu | Synthesis and characterization of a series of biodegradable and biocompatible PEG-supported poly(lactic-ran-glycolic acid) amphiphilic barbell-like copolymers[END_REF] . This stiffening continues during degradation until separations phases are complete, or until degradation becomes preponderant. This last point is eased by the molecular weight decrease observed during the first 3 weeks (Figure 4, 50% decrease) that facilitate micro-domains rearrangements. Evolution of the work necessary to load and unload the material at 10, 20 and 50% was calculated to measure the influence of the hysteresis of the material. As for the stiffness, the amount of work becomes greater after some weeks before drastically decreasing, illustrating the loss of mechanical properties. Work curves decrease was more important than the stiffness one. During degradation, polymer chains were shortened, but kept a good stiffness modulus. While properties with large deformation (illustrated by work) were lowered because of untangled chains. The loss of mechanical properties is not important between the first and the eighth week ensuring the keep of enough mechanical properties of the RIBS and its efficiency. But as seen previously (Figure 4), after 10 weeks, the polymer has lost more than 90% of its initial molecular weight, making mechanical tests impossible due to the extreme brittleness of the specimens. Finally, after 10 weeks, the material would lose the main part of the mechanical properties, meaning that the mechanical resistance should be performed by the constructs composed of infiltrated cells and remaining components of the RIBS.

CONCLUSION

In present study, we chose PLA-b-PEG-b-PLA as RIBS due to mechanical and degradation properties corresponding to the specifications required for biliary stents. We found no influence of pH on the kinetics of degradation for PBS (pH 7.2) and simulated bile fluid (pH 8.4), with in particular the material remaining impermeable for at least 8 weeks, and keeping its mechanical properties for 10 weeks. In vitro degradation was complete at 6 months. Results of present study proved that PLA-b-PEG-b-PLA RIBS had the required in vitro degradation characteristics to secure the biliary anastomosis in liver transplantation. In vitro results will be used as a guideline for planning later in vivo studies.

Compliance with Ethical Standards:

• Conflict of Interest: The authors declare that they have no conflict of interest.

• This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Ackowlegments: M-P. Montmasson for the simulated bile fluid, J-P. Alcaraz for the horizontal diffusion chamber, S. Hunger for the size exclusion chromatography tests, G. Machado and Q.

Breche for help for mechanical tests.

2. 4 .

 4 At defined time-points, compressive mechanical tests were realized at a controlled temperature of 37 °C on the RIBS over the degradation period. To match with set-up experimental size, RIBS samples of 5 mm length were tested. The test was run in triplicate for each sample. Mechanical tests consisted in 3 successive cycles, load at strain level 10, 20 and 50% respectively, with a loading speed rate of 6 mm/min followed by an unload with a speed rate of 0.05 mm/min. Mechanical tests were performed with a Gabo Eplexor mechanical test machine with a load cell of 25 N at 0, 1, 2, 3, 4, 6, 8 and 10 weeks of degradation. To measure the strain field, a Digital image correlation software Vic2D was used to measure the section deformation of the RIBS. During mechanical tests, images of the specimens were recorded with a camera at a frequency of 30Hz. The mechanical work (N.m) to deform the RIBS was evaluated it was calculated by means of the area under the force-displacement curve.

Figure 1 :

 1 Figure 1: RIBS manufacturing. A-Films made by solvent evaporation. B-Film-rolling and gluing thanks to a partial dissolution of the polymer film edges. C-Finalized RIBS.

Figure 2 :

 2 Figure 2: Horizontal diffusion chamber. A: water column, B: diffusion chamber with degradation fluid, C: 37°C independent liquid circuit. D: Sample to test, surrounded by cellulose joints.

Figure 3 :

 3 Figure 3: Weight loss and water uptake of PLA-b-PEG-b-PLA triblock copolymer during 12 weeks of degradation at 37°C. Solid line: 'control group' with PBS (pH 7.2) as degradation solution,

Figure 4 :

 4 Figure 4: Molecular weight and dispersity index evolution of PLA-b-PEG-b-PLA triblock copolymer during 12 weeks of degradation at 37°C. Solid line: 'control group' with PBS (pH 7.2) as degradation solution, dotted line: 'biliary group' with bile like serum (pH 8.4). (Data are represented as means ± SD with n=3).

Figure 5 :

 5 Figure 5: Mechanical compression tests: 3 successive cycles with load at 10, 20 and 50% strain level, followed by an unload to zero strain. A. Typical result of radial compression test on a RIBS. Stiffness (slope of curve at the origin in red) evaluated for each deformation cycle. B. Same mechanical test applied on a silicone stent segment.

Figure 6 :

 6 Figure 6: Stiffness (K) for RIBS mechanical compression tests during degradation, for different strain cycles.

Figure 7 :

 7 Figure 7: RIBS compressive mechanical tests. Work evolution during degradation for RIBS (R) in black, compare to work for silicone stent (S) in red.