Pierre - Edouard Osche
email: pierre-edouard.osche@loria.fr

Sylvain Castagnos
email: sylvain.castagnos@loria.fr

Anne Boyer
email: anne.boyer@loria.fr

From Music to Museum: Applications of Multi-Objective Ant Colony Systems to Real World Problems

Keywords: Recommender Systems, Multi-Agent Systems, Multi-Objective Sequences, Music Online Services, Cultural Heritage

Recommender systems are a flourishing domain in computer science for almost 30 years now. This rising popularity follows closely the number of data collected all around the world. Each and every internet user produces a huge amount of content during his lifetime. Recommender systems proactively help users to navigate these pieces of information by gathering, and selecting the items to users' needs. In this paper, we discuss the possibility and interest of applying our Multi-Objective Ant Colony System called AntRS to recommend items in different application domains. In particular, we show how our model performs better than the state-of-the-art models with music dataset, and describe our work-in-progress with the museum of fine arts in Nancy (France). The motivation behind this change of application domain is the recommendation of progressive sequences rather than unordered lists of items.

INTRODUCTION

Noah, an athletic young man, decided to listen to music while running, and found the perfect app for that. It allowed him to generate a playlist of recent songs that are adapted to his preferences. This application knew how to renew its recommendations from one session to another making him discover new music while, in the same time, proposing titles that he already knew and loved.

A few blocks away, Kate decided to go to a museum before her next university course. As she had only 2 hours free, she installed on her smartphone the mobile application provided by the museum to be recommended an ideal path taking into account both her eclectic tastes and her aversion to the crowd. She was willing to travel longer distances to avoid congestion points. But most importantly, she did not want to miss her favorite painting.

The same scientific problematic is behind these 2 stories: being able to provide adapted and coherent sequences to users. The target state can be a relevant painting to see, a museum exit to reach or an energetic song to recommend when finishing the race. But the way users get to this target state is also important. The sequences should be as personalized and progressive as possible while offering a good compromise between multiple objectives (precision, diversity, density of population and distance within the museum for Kate; precision, novelty, serendipity and music features such as recency, and tempo for Noah).

To address these issues in the music application domain, we proposed a multi-objective recommender system called AntRS [START_REF] Osche | AntRS: Recommending Lists through a Multi-Objective Ant Colony System[END_REF].

The latter belongs to the multi-agent system family in which agents wander through a graph where nodes represent the items of the domains (music titles) and edges represent links between those items. AntRS is a multi-objective model because it integrates several classic objectives considered for a good recommendation (similarity, diversity, novelty, preferences), and searches for an optimum between all of them. In this paper, we aim at investigating the generic nature of our model. We argue that it is possible to add or remove objectives on the fly, and that AntRS can be applied on different domains. In this paper, we thus propose to extend AntRS with new results showing the flexibility of our model through a new dimension called progressiveness. We also discuss the possibility to translate our model to another application domain (cultural heritage) which is an on-going research.

This paper is organized as follows: Section 2 presents the related work on multi-objective recommenders and their application in music and museum domains. Section 3 describes our AntRS model. Section 4 describes the experiments carried out and the results obtained in music as well as our plan to apply our model in the museum space. Finally Section 5 concludes this paper and presents our perspectives.

BACKGROUND 2.1 Ant Colony Systems

The Ant Colony Optimization algorithms (ACO) are Nature-inspired programming algorithms that computationally reproduce the pheromone communication between ants to find shortest paths between a starting node and a target node. Our model, called AntRS, is derived from one of those systems: the Ant Colony System (ACS) algorithm [START_REF] Dorigo | Ant colony optimization[END_REF]. The latter relies on a pseudo-random proportional rule to favor exploitation of the pheromone information, and a local pheromone update to diversify the search performed by ants during one iteration. In other words, each time an ant takes an edge, it deposits some pheromones along its way, regardless of the quality of the path. As explained by Dorigo, this version of the ACO algorithms is known to "decrease the pheromone concentration on the traversed edges, thus encouraging ants to choose other edges and, hence, to produce different solutions. This makes it less likely that several ants produce identical solutions during one iteration". We took inspiration from the ACS algorithm so as to identify relevant items in the very large exploration space of online services (e.g. millions of songs on music streaming services, and hundreds of paintings in a museum), recommend them to users, and evaluate the quality of recommended lists through several joint metrics (precision, diversity, novelty...). We refer the reader to the Dorigo and Birattari paper [START_REF] Dorigo | Ant colony optimization[END_REF] for all the details about the model as we will use some of the notations/equations of their work in the section 3. In the recent years, many studies have been using multi-agent systems and more specifically the ACO algorithms. One of the first study using the ACO in recommender systems was from Semet et al. [START_REF] Semet | Ant colony optimisation for e-learning: Observing the emergence of pedagogic suggestions[END_REF] in an e-learning system. The authors built a graph where the nodes represent educational resources and the edges have transition probabilities associated to them. The authors also introduce success and failure pheromones as an additional information. The system could however be improved as there is no user model and it also needs professors to evaluate the possible paths, which could be an important drawback in a large database. Optimization problems have also been tackled by ACO algorithms with success. We can cite [START_REF] Luca | MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows[END_REF] which proposed a framework to use multiple ant colony system for the vehicle routing problem with time windows, a classic multi-objective problem where multiple objectives are conflicting with each other. Since this paper is more focused on applying our model in two different domains (music and museum), the next two subsection will focus on recommender systems in these particular domains.

Recommender Systems in Music

When it comes to recommending music, a system can either propose a list of independent items at each time step, or it can suggest a sequence of items [START_REF] Quadrana | Sequence-Aware Recommender Systems[END_REF]. Let us note that Sequence-Aware Recommender Systems may refer to the order of the past events (i.e. looking for co-occurrence patterns [START_REF] Bonnin | Automated Generation of Music Playlists: Survey and Experiments[END_REF] or for sequential patterns [START_REF] Hariri | Context-aware Music Recommendation Based on Latenttopic Sequential Patterns[END_REF] in past sessions) or the order of the future recommendations (such as in playlists [START_REF] Jannach | Beyond hitting the hits: Generating coherent music playlist continuations with the right tracks[END_REF][START_REF] Maillet | Steerable playlist generation by learning song similarity from radio station playlists[END_REF]). As recent research has found little evidence that the exact order of songs actually matters to users [START_REF] Tintarev | Sequences of Diverse Song Recommendations: An Exploratory Study in a Commercial System[END_REF], we first limited our state-of-the-art to the recommendations of lists.

Besides its ability to generate recommendation lists, our system sees the selection of relevant items as a multi-objective optimization problem. Most recommenders solely focus on the accuracy (precision and recall) [START_REF] Ricci | Recommender Systems Handbook[END_REF]. Yet, more and more systems attempt to find a compromise between several dimensions such as precision, serendipity and novelty [START_REF] Kaminskas | Diversity, Serendipity, Novelty, and Coverage: A Survey and Empirical Analysis of Beyond-Accuracy Objectives in Recommender Systems[END_REF], or between precision and diversity [START_REF] Amaury | Understanding Usages by Modeling Diversity over Time[END_REF][START_REF] Ziegler | Improving recommendation lists through topic diversification[END_REF] for example. There are several ways to address this issue. One can either look for a set of Pareto solutions, considering that a solution is optimal if it is not possible to make any objective better off, without making at least one objective worse off [START_REF] Zuo | Personalized Recommendation Based on Evolutionary Multi-Objective Optimization [Research Frontier[END_REF]. In that case, the goal of recommender systems is to produce as many solutions as possible from the Pareto-front solution set. Or one can rank the items in a single list by aggregating or reordering the results of each objective taken separately [START_REF] Tulio Ribeiro | Pareto-efficient Hybridization for Multi-objective Recommender Systems[END_REF]. This list can be computed at once [START_REF] Guimarães | GUARD: A Genetic Unified Approach for Recommendation[END_REF], or come out of a 2-step process consisting in building several lists of candidate items for the active user and in merging them [START_REF] Silva Fortes | User-Oriented Objective Prioritization for Meta-Featured Multi-Objective Recommender Systems[END_REF][START_REF] Geng | NNIA-RS: A multi-objective optimization based recommender system[END_REF][START_REF] Tulio Ribeiro | Multiobjective Pareto-Efficient Approaches for Recommender Systems[END_REF][START_REF] Wang | Multiobjective optimization for long tail recommendation[END_REF][START_REF] Wang | Decomposition based multiobjective evolutionary algorithm for collaborative filtering recommender systems[END_REF][START_REF] Xia | Multi-objective Mobile App Recommendation: A System-level Collaboration Approach[END_REF]. Recommending several Pareto solutions offers the advantage to leave the choice to the active user. It can be interesting in some application domains such as e-commerce where an explicit validation process from the user is mandatory. However, in the context of online music services, it is not conceivable to request a user decision at each timestep. The songs must come one after another without disturbing the user in his/her main current task. For this reason, we focused on recommenders which produce only one solution (i.e. only one list of recommendations).

As a conclusion, our model AntRS is a multi-objective single-list recommender. Those recommenders usually suffer from several limitations: they are dependent from the application domain (any change in the set of objectives has a drastic impact on the implementation of the model) and they are very time-consuming. To bypass these difficulties, we rely on a Multi-Agent System (MAS), and more precisely on an Ant Colony System explained below. MAS have multiple advantages in our context such as the low computational complexity, the ability to tackle multi-objective problems and the resilience to changes. In this paper, we first deepen the results we got on a music dataset in [START_REF] Osche | AntRS: Recommending Lists through a Multi-Objective Ant Colony System[END_REF]. Then, we show how this model can be translated to another application domain. We chose to apply AntRS to Cultural Heritage, and more specifically to museum guides, since the visitors' lists of recommendations should notably be ordered in sequences so as to minimize the distance to travel and to tell a coherent story. Thus, this change of context allows us to extend our model with the notion of progressiveness.

Recommender Systems in Museums

In the recent years, a trend emerged in recommender systems because experimentations showed that users needed more than precise recommendations. Metrics like diversity, novelty, serendipity slowly were more and more considered into recent systems alongside user's contextual information (Is the user alone? Is she/he at work or at home? . . . ) with Context-Aware Recommender Systems (CARS) [START_REF] Adomavicius | Context-aware recommender systems[END_REF]. This recent trend follows the development of technologies capable of feeding models with contextual and geographical information like smartphones, GPS or indoor positioning system [START_REF] Deak | A survey of active and passive indoor localisation systems[END_REF]. The recommender systems that take into account all of these pieces of information are gathered under the name Location-Aware Recommender Systems (LARS) [START_REF] Levandoski | Lars: A location-aware recommender system[END_REF].

The tourism domain is an obvious choice to field test algorithms taking into account the context and the location of user in a real physical environment. As early as the beginning of the 2000s, some experimentations were conducted in e-tourism to help visitors find their way to interesting areas. Cheverst et al. [START_REF] Cheverst | Developing a context-aware electronic tourist guide: some issues and experiences[END_REF] were one of the first to propose a system taking into account contextual information (location, date, hour of the day, opening and closing hours for attractions,. . . ). However, no visitor model were created and, thus, no recommendation were made. Chou et al. [START_REF] Chou | Semantic web technologies for context-aware museum tour guide applications[END_REF] propose a system were works of art are modelled as well as the visits themselves. They then used these data to model visitors preferences and recommend them works of art, areas of interest or even a route. To model visitor preferences, studies have shown that viewing time is correlated with interest for simple item like clothes. Though it still has to be tested with more complex items like exhibits (i.e. it might be easier and less time-consuming to tell if we like a t-shirt or not compared to a 5x3m painting).

In the recent years, a lot of studies expanded the work already done by using new technologies as well as advancement in recommender systems in general. Some of those studies are particularly interesting for our current work. For example, Van Hage et al. [START_REF] Van Hage | Finding your way through the rijksmuseum with an adaptive mobile museum guide[END_REF] created a model capable of guiding visitors through the Rijksmuseum in the Netherlands. The algorithm takes into account the visiting time specified by the visitors, the ratings given on already seen exhibits or the distance between the different items available for the recommendation. However this study lacks some important points: the authors only simulated the visit and visitors had to manually rate what they saw to feed the recommender system, potentially degrading the user experience. Woerndl et al. [START_REF] Woerndl | A model for proactivity in mobile, context-aware recommender systems[END_REF] tried to alleviate this problem by creating an algorithm which proactively proposes recommendation to the user based on internal metrics computed on contextual information. Nonetheless, the users still had to validate afterwards if the recommendation was made at a good moment or not.

Some studies focused on other subject specific to tourism like how the crowd might impact the visitor experience and how to manage it as best as possible [START_REF] Naudet | Personalisation in crowd systems[END_REF]. The authors in [START_REF] Yoshimura | An analysis of visitors' behavior in The Louvre Museum: a study using Bluetooth data[END_REF] performed an extensive study in the Louvre museum on more than 24,000 visitors with Bluetooth sensors and a mobile application to track their location, giving some interesting insights on the behavior of the visitors. Based on the duration of their visit, the visitors were divided in two groups: the short-stay and the long-stay visitors. It was found that these two groups, despite not having the same visiting time, were mostly looking at the same works of art and taking the same paths. These findings illustrate the importance of having a way to manage the crowd.

Finally, other studies highlighted how a single person may behave while visiting a museum. Veron and Levasseur [START_REF] Véron | Ethnographie de l'exposition: l'espace, le corps et le sens[END_REF] in an ethnographic study in the Centre Georges Pompidou were able to categorize four visiting style: (1) the ant who looks at every artwork in the scenography order, (2) the butterfly who performs a zigzag visit, alternating between each side in a room, (3) the grasshopper who progresses in the museum by doing big leaps to only look at a few selected pieces interesting to him, and (4) the fish who stays at the center of the room to have a quick look from away to all the exhibits before going into another room. Recent studies have tried to retrieve or to use these visiting styles in recommender systems. Like so, the authors in [START_REF] Kuflik | Analysis and Prediction of Museum Visitors' Behavioral Pattern Types[END_REF] did an experiment where 140 visitors were put in a room with paintings and an audio-guide. Based on how the visitors behave, the authors conclude that the four visiting style were retrieved and that it was possible to predict the visiting style of a single visitor relatively early. They nuanced their results because, unless [START_REF] Véron | Ethnographie de l'exposition: l'espace, le corps et le sens[END_REF], they showed that visitors were able to change from a visiting style to another during the visit. This study did however not include a recommender system. Finally, Lykourentzou et al. [START_REF] Lykourentzou | Improving museum visitors' Quality of Experience through intelligent recommendations: A visiting style-based approach[END_REF] developed a simulation were entities wandered through a virtual museum based on the four visiting styles. They then showed that with intelligent recommendations, it was possible to increase the satisfaction of the entities at the end of the visit. The study was however not verified in a real life setting.

ANTRS MODEL

AntRS has been built with several goals in mind: (1) be as generic as possible, (2) be able to include several competing objectives in a single list, (3) be resilient to changes in the environment (new items, new preferences,. . . ). As explained previously, our model takes inspiration from the ACS algorithm because the latter gathers all the quality needed to satisfy those objectives. However, we want to point out the differences between the classic ACS and our model AntRS. In this section, we will outline those differences as well as new results in comparison to our previous study.

Graph creation

The first step before running our model is to create the graph the agents will roam on. To do so, we created nodes corresponding to items of the domain and applied a selection algorithm to create edges between these nodes, as working with a complete graph was beyond the realm of possibilities giving the usually huge number of items. At this point, we formulated two assumptions to help us construct the graph: (A1) past sequences created by previous users represent useful domain knowledge which should be exploited, and (A2) past sequences done by previous users are not always the best possible ones and could have been improved with clever recommendations. The general intuition behind these two assumptions can be explained like so:

• (A1): users consult items that satisfy their needs in the best possible way, thus there is interesting patterns and knowledge to exploit from these consultations; • (A2): given that users do not generally browse all the existing items to select the perfect ones for their needs, it is safe to assume that another sequence could have satisfied the needs of users in a better way.

However in this work, we did not prove or disprove these assumptions, we simply used them to help building our graph.

To take into account these two hypotheses, we first computed the number of transitions (i.e. co-consultations) between each pair of items in our dataset. We added all the transitions above a specific threshold, and only some of those below this threshold as edges. Finally, if a given connectivity degree was not reached, we added new edges between items who were not connected in our dataset to allow our model to discover new potential interesting paths not known by users. The process of creating an edge is shown in Equation 1.

e i j =              if t i j ≥ m
or if t i j < m and q < t i j where q ∈ [min t il ; log(max t il )] or if t i j = 0 and if deд(i) < d then pick a random transition until deд(i) = d (1) where e i j is the presence of an edge between vertices i and j, t i j is the number of transitions performed from item i to item j by the users in the dataset, m is the threshold where transitions are not directly added to the graph as edges, q ∈ [min t il ; log(max t il )] is a random variable uniformly distributed, min t il is the minimal number of transitions between the item i and all the others items l ∈ V i where at least one transition has been found, deд(i) is the current degree of the node i in the graph and d is a parameter specifying the minimal degree each vertex must have in the final graph.

For our first study in [START_REF] Osche | AntRS: Recommending Lists through a Multi-Objective Ant Colony System[END_REF], we only created one graph using all the data available with all the training users. This choice was justified by the fact that it takes less time to do so as the graph can be huge. Moreover, the edges in the graph reflect the global knowledge of all the user in the system. In this paper, we tested another way to proceed by creating a graph per test user. To do so, we computed the n most similar neighbours of the active user based on the known ratings with a classical cosine similarity measure. Those n users were then used to create the graph as explained above.

Objectives

It is now widely admitted that the sole precision is not sufficient to produce good recommendations to users. In [START_REF] Osche | AntRS: Recommending Lists through a Multi-Objective Ant Colony System[END_REF], we proposed to define a set of 4 concurrent objectives that often have to be considered in the literature while recommending a list of items. In this paper, we aim at showing that these objectives are transposable in different application domains, guaranteeing the generic nature of our approach. For the purpose of this study, we also added a fifth objective -called progressiveness -whose relevance will be discussed depending on the application domain.

The ability to add objectives, modulate their importance or remove them on the fly is essential for having an adaptive model. To address this issue, we chose to include as many colonies as objectives in our model where each colony is specialized in maximizing its own objective. To do so, we modified the way the ACS model computes the distance d between two nodes of the graph. The rest of this Section describes the equations used to compute the distance for each colony.

Similarity -The goal of this colony is to find items as similar as possible of what the user previously viewed or is currently viewing. A lot of methods exist to compute the similarity of two vectors and, based on our dataset and on the metadata available, we decided to use a cosine similarity measure [START_REF] Su | A survey of collaborative filtering techniques[END_REF]. To compute the distance value on the edges of the graph, we simply computed the cosine similarity between the two items represented by the vertices. More formally, for an edge (i, j), its associated distance d i j is computed with the cosine similarity between the vectors of the descriptive characteristics of the items i and j.

d i j = 1 sim(C i , C j ) (2)
where C i are the characteristics of the item i. The item characteristics depend obviously on the dataset and on the meta-information available but, we can formalize that each item of the dataset is described by n characteristics as follow C i = {c 1 , c 2 , . . . , c n }. We used the multiplicative inverse to transform the similarity metric sim ∈ [0; 1] into a distance d ∈ [1; +∞]. Therefore, a distance value near 1 on an edge (i, j) means that the two items i and j are similar.

Diversity -This characteristic and the similarity are often described together as they are both related to the distance/correlation between the items liked by the user and his recommendations. But unlike similarity, diversity depicts how dissimilar two items are relatively to each other. Similarity and diversity are complementing each other in the sense that they are both needed to adapt the system to the needs of different users [START_REF] Jones | User Perceived Qualities and Acceptance of Recommender Systems: The Role of Diversity[END_REF]. To compute this objective, we chose to apply one of the classic diversity metric which is obtained by computing the inverse of the similarity between two items, as shown in Equation 3. As for the similarity, we used the multiplicative inverse of the diversity to obtain a distance d ∈ [1; +∞].

d i j = 1 1 -sim(C i , C j ) (3)
Novelty -The goal of this colony is to search for items that are not yet known by the user. Novelty is an important characteristic of a recommender system to avoid a potential lack of interest of users due to too much foreseeability in the recommended items [START_REF] Vargas | Rank and relevance in novelty and diversity metrics for recommender systems[END_REF]. To determine if an item is novel or not relatively to a specific user, we used the work of Zhang [START_REF] Zhang | The Definition of Novelty in Recommendation System[END_REF] who defined the novelty as a notion composed of three characteristics: (1) Unknown: the item is unknown to the user, (2) Satisfactory: the item is liked by the user, (3) Dissimilarity: the item is dissimilar to the other items known by the user. The author proposed to evaluate the novelty of the item i for the user u as follow:

novelty(i, u) = p(i |unknown, u) • dis(i, pre f u ) • p(i |like, u) (4)
where p(i |unknown, u) is the probability that the user u does not know the item i, dis(i, pre f u ) is the dissimilarity between i and the set of items in the users' profile and p(i |like, u) is the probability that u will like i. However, the dissimilarity and the satisfaction of the user relatively to i are closely related to other objectives in our model, respectively maximized by the diversity colony and by both the preferences and the similarity colonies. Hence we decided to trim down the Equation 4 to the probability p(i |unknown, u) only (see Equation 5).

p(i |unknown, u) = -loд(1 -pop i ) (5)
where pop i is the popularity of item i.

Preferences -The preferences characteristic corresponds to what the user really likes. It intersects with the similarity notion but, again as with diversity and novelty, we think that preferences express another aspect of a good recommendation for a user. The similarity characteristic allows the recommender to propose items that are similar to the preferences of the user, but it is not guaranteed that she/he will like those items. It is for example perfectly common to both like and dislike some songs coming from the same album and artist, yet those songs will probably be treated as very similar relative to each other. The preferences characteristic favors items that are known to be liked by the user.

The goal for this colony is to find a sequence in the graph prioritizing items that are already known to be liked by the user. Thereby, items must have criteria conveying how the user like an item or not. This can be done either with explicit feedback (e.g. item rating,. . . ), with implicit feedback (e.g. number of times the user viewed an item,. . . ) or with a combination of both. The nature of the feedback will heavily depend on the domain, but we can formalize that each collected information concerning the behavior of a user on an item must be taken into account. Let C u be the set of criteria representing all the actions that a user u may perform on the items of the system, thus c u,i is the sum of all interactions specific to a single criterion c that a user u performed on an item i (e.g. the number of times a user u viewed i). To aggregate all the different interactions possible in a single value, we use the presumed interest formula proposed by Castagnos et al. in [START_REF] Castagnos | A client/server user-based collaborative filtering algorithm: Model and implementation[END_REF] and described in the Equation 6.

presumed interest u,i = v min + c ∈C (w(c) • c(u, i)) c ∈C w(c) • (v max -v min ) c max (6
) where c(u, i) corresponds to normalized values given to the item i by the user u to each criterion c, w(c) is the weight of the criterion c, v min and v max are the minimal and maximal expected values for the presumed interest and c max is the maximal value that c(u, i) can take regardless of the criteria. In our case, we considered the following criteria for each song: number of consultations, number of skips, number of bans (when the user do not want to listen to the song ever again), and number of likes.

Progressiveness -While the majority of the recommender systems propose a list of items ranked from most likeable to less likeable, we think that an ordered sequence of items could be more useful to the user in some specific domain. While a simple top-n list is generated from a single starting point, which is usually the user model at a time t, a well-crafted sequence will have a starting point, an ending point and a meaningful path to go from the former to the latter. In certain domain like e-education, recommending a progressive enough sequence (i.e. a sequence of courses progressing through skill level neither too slow nor too fast) is a key element to guarantee the user a good learning experience. One of the key element to a sequence is the progression between each item: a too slow progression and the user will stagnate, a too fast progression and she/he could be lost or feel that there is no progressiveness at all in the recommended list of items. In the context of cultural heritage, the progressiveness can be linked to the distance to go in a museum and/or to the semantic links between items so as to tell a coherent story through the recommended tour.

Progressiveness colony -The concept of progressiveness is tied up to our goal of finding a good sequence of items. Contrary to the majority of recommender systems, we not only want to provide a list of items but a sequence having a beginning, an end and where each item makes sense one to another. As stated before, in a museum, a good recommended sequence could consist of exhibits related in one way or another (i.e. from the same artist or from the same period) and located close to each other. Such a sequence could then slowly progress to another artist or a different section of the museum. Thus our goal is to recommend a sequence that is progressing neither too slow nor too fast: we call this the optimal progressiveness o. This metric is used to ensure that the agents of the progressiveness colony find a tour where each node offer a good progressiveness in relation to its predecessor and successor nodes. To do so, we computed o based on the first and the last items of a given sequence for a specific user.

o n = c z n -c a n s (7)
where o n is the optimal progressiveness value of the nth characteristic of a specific sequence, c z n is the nth characteristic of the last item z of the sequence, c z n is the same for the first item of the sequence and s is the number of items in the sequence. The Equation 7 will be applied for the m item characteristics, resulting in a m-sized vector of optimal progressiveness values (o

1 , o 2 , • • • , o m )
for the specific sequence. This vector will then be used in the calculation of the distance of an edge (i, j) for the progressiveness colony. This method implies to have numerical characteristics to apply the equation, like for example the tempo of a music track or the date of a painting.

The optimal progressiveness o value is then used to compute the distance d between two nodes of the graph.

d i j = m n w o n • c jn -c in o n m n w o n ( 8
)
where m is the number of item's characteristics considered, o n is the optimal progressiveness value of the nth characteristic for the sequence, w o n is the weight of the nth characteristic for the user and depending on his preferences and c j n is the value of the nth characteristic of the item j.

Merging tactics

In the previous section, we described five objectives that could provide suitable recommendations for users. Each of these five objectives is associated to a specific ant colony in our model. Thus, after this step, we are left with as many lists of recommendations as colonies, where each one should represent a part of the final recommended list. In order to build it, we needed a tactic to merge all the colonies' lists into one. To do so, we propose two techniques described below.

Merging colony -The first merging tactic relies once more on the ACS algorithm but with one additional colony that we called "merging colony". Starting from the set of items found by the other colonies (step 1), the merging colony considers all the objectives at once with a weighted sum to calculate the distances on the graph's edges (step 2), as shown in Equation 9.

d i j = col ∈colonies w(col) • d i j (col) (9)
where w(col) is the weight representing the expected importance of the colony's objective in the final recommendation. To estimate those weights, we calculated the average values of each objective (similarity, diversity, novelty and preferences) on the last n sessions processed of the user. This gave us the general importance of each objective while taking into account contextual information and recent tendencies in the user's behavior. We also built a new graph for this path of the algorithm. To construct it, we used all the items in the lists found by the other colonies as vertices, we added edges to each consecutive pair of items in the lists and finally we added random edges in the same way that is described in the last part of the Equation 1 to give the possibility of new paths to be found and chosen by the merging colony's agents.

Lists merging -For the second merging tactic, we calculated the weight w(col) of each objective in the same way that for the merging colony (see above). We then built the list step by step by considering all the items found by the different colonies. We iterated through all the available items for each step of the list construction and we added to the final recommended list the item which yield the best amelioration towards the expected values. This process was stopped either when the remaining items degraded the list's metrics, when there was no items left or when the last item of the initial listened session was found.

EXPERIMENTS IN DIFFERENT APPLICATION DOMAINS 4.1 Music

Our first evaluation of AntRS was done in the music domain due to the ease of getting data [START_REF] Osche | AntRS: Recommending Lists through a Multi-Objective Ant Colony System[END_REF]. We will not discuss the results obtained in this study which showed the legitimacy of our multi-objective approach represented by separate colonies, thus we refer the reader to our last article [START_REF] Osche | AntRS: Recommending Lists through a Multi-Objective Ant Colony System[END_REF]. In this paper, we will present the results obtained with two major differences in comparison to our previous study: we changed the way users are selected to build the graph in the training set so as to validate the robustness of our model, and we built a new graph for each user rather than having the same graph for all users to improve performances. We used the same dataset as previously from Deezer with 3,561 unique users, 178,910 unique songs, and 1,871,919 listenings from which we randomly chose 500 users to work with. But first, let us describe how we proceed to evaluate our model.

We compared the performances of AntRS with four state-ofthe-art algorithms capable of producing lists of items in the same conditions than our model. The first three are classical techniques spanning most of the work in the recommender systems domain: UserKNN [START_REF] John S Breese | Empirical analysis of predictive algorithms for collaborative filtering[END_REF], TrustMF [START_REF] Yang | Social collaborative filtering by trust[END_REF], and SVD++ [START_REF] Koren | Factorization meets the neighborhood: a multifaceted collaborative filtering model[END_REF]. Those three algorithms were implemented using the Java library librec [START_REF] Guo | LibRec: A Java Library for Recommender Systems[END_REF]. We also implemented a fourth hybrid multi-objective model named PEH described in [START_REF] Tulio Ribeiro | Multiobjective Pareto-Efficient Approaches for Recommender Systems[END_REF] to be able to compare AntRS to a state-of-the-art multi-objective recommender system. We used the three algorithms described above in the hybridization process. In the first study, we performed all the tests on a cross-validation dataset with a training set of 400 users and an evaluation set of 100 users each time. The goal was to test our model in a situation where it did not know anything about the new user. We obtained good results, showing that our model was indeed capable of producing recommendations to new users. For this paper, we used an approach were 80% of the user sessions were in the training set and the last 20% were the evaluation set with the same cross-validation method. The goal was to prove that our model is also capable of producing good results in a more classical setting used by the majority of the domain studies. Either way, for each listening session composed of 5 items or more in the test base, a recommended session was produced. The users of the training base had listened to 10,621 sessions while there were 2,569 sessions in the test base.

We used different metrics capturing all the aspects of what we consider a good recommendation: Precision, Recall and F-measure [START_REF] Baeza-Yates | Modern information retrieval[END_REF], Similarity and Intra-list Similarity [START_REF] Ziegler | Improving recommendation lists through topic diversification[END_REF], Diversity and Relative diversity [START_REF] Mcginty | On the Role of Diversity in Conversational Recommender Systems[END_REF][START_REF] Vargas | Rank and relevance in novelty and diversity metrics for recommender systems[END_REF]. We also used the preferences and the novelty metrics of Equations 5 and 6 as well as in [START_REF] Vargas | Rank and relevance in novelty and diversity metrics for recommender systems[END_REF].

As explained in Section 3, we also proposed and tested two merging tactics to combine the results of our four objectives. We also tested to run the merging colony alone, without the step 1 in the first merging tactic of Section 3.3: in that scenario, the merging colony operates on the whole graph, rather than on the subgraph of items recommended by the four colonies.

We also tested a new version of our model where, instead of building a single graph for all the users (AntRS single-graph) we built one graph per user based on the n nearest neighbors, as explained in section 3.1 (AntRS multi-graph).

In Table 1, we present the summary of the results obtained for all the models tested and their variations. In our test, we used only the four first objectives colonies (similarity, diversity, novelty, preferences) without the progressiveness. We will explain why at the end of this section.

From the results, we can see that both AntRS variations obtain the best precision, recall and F-measure of all the models tested, which means that our model is the best to capture the preferences from the lists initially listened by the users in the training set. AntRS also outperformed the other models for the diversity, novelty and preferences metrics, while still managing to maintain a correct level of similarity. We can also see that AntRS multi-graph manages to obtain almost the same performance as AntRS single-graph. We explain this small disparity by our selection of the n neighbor which could be improved along with the number of users for this experience (i.e. if the single graph was built with a lot more users than 500 then a selection process for the users could be useful).

Finally, let us talk about the progressiveness colony. As we stated earlier, we did not include it in the experiment for two main reasons. First, we ran some tests beforehand and the results were not conclusive. The colony obtained a very poor accuracy without building apparent progressive sequences. To understand why, we looked at the original music sessions that the users listened to. With the help of the Mann-Kendall test, which is designed to detect monotonic upward on downward trend of a variable over time, we found that there was no monotonic trend in the sessions. These results match with the recent research done in music showing that the order of songs is of little importance to users in playlists and music radios [START_REF] Schedl | Current challenges and visions in music recommender systems research[END_REF][START_REF] Tintarev | Sequences of Diverse Song Recommendations: An Exploratory Study in a Commercial System[END_REF].

Museums

After the music experimentation and to prove that our model is generic, we now want to apply it to a new domain: cultural heritage. This is a sensible choice as recommendation in tourism is booming since the 2000s and we wanted to work in a partnership with a museum in our city. Furthermore, the cultural heritage brings a lot of new challenges that are specific to the physical space represented by a museum, like for example managing the crowd in the museum, taking into account the physical space of the museum, taking into account the state of the visitor (young, old, tired, in a hurry, . . . ). In this section, we will describe the museum, the experience we are currently doing, the data we are collecting and what we plan to do with these data.

The museum -We are currently working with the museum of fine arts1 in Nancy, France. This museum is well-known for its fifteen century to today collection of paintings, statues and modern art works. It has close to 130,000 visitors each year which are welcomed in a 9.000m 2 classified historic building. The museum permanently presents about 400 works of art, without counting those stored in the archives. We currently have a partnership with the museum where we have access to their internal resources (information on pieces of art like artist, date of creation, title and so on). The museum also granted us a full and free entry for us and the experimentation's subjects.

Experimentation -As we said earlier, an experimentation is ongoing in the museum of fine arts. We are currently recruiting people to visit the museum. To analyze their route, we considered three possible solutions: (1) a manual tracking with someone following the visitor and noting his positions, like in [START_REF] Véron | Ethnographie de l'exposition: l'espace, le corps et le sens[END_REF], (2) an indoor tracking device with the help of a smartphone application or RFID/bluetooth technologies, as explained in [START_REF] Farid | Recent advances in wireless indoor localization techniques and system[END_REF], and (3) an eye-tracking device. We decided not use the first solution as it necessitated a lot of work without giving a better accuracy in the data. We also did not choose the indoor tracking system because we did some internal testing with smartphone tracking as well as bluetooth beacons and the results were not good enough for our needs. We could not get those devices to have a better precision resolution than a few meters, making them suitable for tracking people in a whole room but not sufficient to precisely know where a visitor is in the room and what she/he is looking at. Thus we chose to use the eye-tracker with the latest version of the Tobii Pro Glasses 2 2 . These glasses allow us to let the visitor relatively free: we do not have to follow him to write down his movements and we do not have to ask him to interact with a tracking device either. The glasses are still a minor inconvenience to wear but it was the best compromise available between tracking precision and visit disruption. Data -In this experimentation, we have two types of data: museum data and visitors collected data. The museum data refers to all the information relative to the museum and to the works of art. We measured the the museum rooms and we also recorded the exact positions of all the works of art. The goal is to be able to recreate the museum virtually and, at least, have a good idea of where the visitor is and what she/he is looking at exactly at each time during his visit. The visitors' collected data refers to the information we are gathering with the experimentation itself. The Tobii Pro Glasses 2 record a video flow of what the visitor has in front of him while, at the same time, compute the fixation points (i.e. what the person is looking at exactly). As we have the video information of where the user is, what she/he is looking at and for how long, we plan to build a dataset where those information will be transcribed as numerical values.

Goals -The goals of this experimentation are multiple. First, we will build a dataset based on the user data collected during the experimentation with the eye-tracker. We aim at providing the community a clean dataset with the information about the museum space, the works of art and also the precise path taken by all the 2 https://www.tobiipro.com/product-listing/tobii-pro-glasses-2/ visitors with timestamp on each movements and stops. With this dataset, we will be able to do offline experiments with our model AntRS to confirm that it is working in another domain. We will be to compute similarity and diversity between pair of exhibits based on their characteristics (artist, period, style, popularity, subject portrayed through the work...), but also based on the co-viewing of exhibits (i.e. we can consider to artworks similar if they are viewed by the same users through their visit). We will also be able to integer the progressiveness of sequences, which was not possible with music. Finally, another area of interest would be to simulate the museum in virtual reality with crowd behavior based on real visitors to try to adapt recommendations to users given their crowd tolerance [START_REF] Lykourentzou | Improving museum visitors' Quality of Experience through intelligent recommendations: A visiting style-based approach[END_REF].

CONCLUSION

In this paper, we showed that AntRS is still obtaining better results than state-of-the-art methods despite switching to a more traditional k-fold method. We also showed that, while not obtaining the very best results, our new approach consisting of creating a graph per user is promising and will probably be the way to go with a larger dataset and some variables tuning. Finally, we discussed about our ongoing experimentation in the museum of fine arts in Nancy, France. This experimentation will allow us to test our model on another application domain to guarantee its generic nature and to test our fifth objective related to progressiveness.

Table 1 :

 1 Experimentations with AntRS as a multi-objective model

			Precision Recall F-measure Similarity	ILS	Diversity	RD	Novelty Preferences Coverage
	AntRS single-graph (4	0.379	0.147	0.205	0.942	0.902	0.058	0.073	0.748	0.631	71.68%
	colonies + lists merg-
	ing)
	AntRS	single-graph	0.339	0.176	0.215	0.943	0.9	0.057	0.085	0.72	0.718	71.68%
	(4 colonies + merging
	colony)
	AntRS multi-graph (4	0.369	0.149	0.203	0.941	0.901	0.059	0.075	0.737	0.633	71.68%
	colonies + lists merg-
	ing)
	AntRS multi-graph (4	0.329	0.167	0.206	0.944	0.905	0.056	0.081	0.707	0.68	71.68%
	colonies + merging
	colony)
	AntRSv1	(merging	0.195	0.121	0.142	0.952	0.931	0.048	0.068	0.307	0.39	71.68%
	colony alone)
	UserKNN		0.213	0.146	0.165	0.947	0.902	0.053	0.085	0.668	0.509	45.5%
	TrustMF		0.214	0.148	0.166	0.947	0.903	0.053	0.085	0.667	0.512	45.48%
	SVD++		0.212	0.147	0.165	0.947	0.903	0.053	0.084	0.667	0.51	45.47%
	PEH		0.196	0.121	0.143	0.952	0.93	0.048	0.069	0.308	0.391	71.68%

https://musee-des-beaux-arts.nancy.fr/accueil-145.html

ACKNOWLEDGMENT

This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 693150.


Barbara Moissa
email: barbara.moissa@loria.fr

Geoffray Bonnin
email: geoffray.bonnin@loria.fr

Sylvain Castagnos
email: sylvain.castagnos@loria.fr

Anne Boyer
email: anne.boyer@loria.fr

Modelling students' effort using behavioral data

Keywords: students' effort, cognitive load, descriptive analytics, eye gaze data, interaction data

come

INTRODUCTION

Decades of studies have shown that student's success is strongly dependent on their effort [START_REF] Hill | Effort and reward in college: A replication of some puzzling findings[END_REF][START_REF] Swinton | The effect of effort grading on learning[END_REF][START_REF] Scariot | Students Effort vs. Outcome: Analysis Through Moodle Logs[END_REF]. Being able to accurately measure students' effort can therefore lead to a better understanding of its relationship with learning outcomes, and to the design of new tools to help teachers identify students who are struggling or not truly engaged in their learning. However, measuring the effort is a particularly difficult task. One difficulty is that despite all the interest raised by this concept, student effort has no widely adopted definition [START_REF] Meltzer | The Impact of Effort and Strategy Use on Academic Performance: Student and Teacher Perceptions[END_REF]. For instance, some define it as just "the amount of studying" [START_REF] Schuman | Comment: Students' Effort and Reward in College Settings[END_REF], while others define it in a more specific manner, e.g., "the amount of time and energy that students expend in meeting the formal academic requirements established by their teacher and/or school" (Carbonaro, 2005).

Not surprisingly, researchers have used a variety of approaches to measure students' effort. These approaches include the time spent on learning tasks [START_REF] Schuman | Effort and reward: The assumption that college grades are affected by quantity of study[END_REF][START_REF] Hill | Effort and reward in college: A replication of some puzzling findings[END_REF] and grades assigned by teachers [START_REF] Nagy | Tracking and Visualizing Student Effort: Evolution of a Practical Analytics Tool for Staff and Student Engagement[END_REF][START_REF] Swinton | The effect of effort grading on learning[END_REF]. Despite being easy to acquire, the time spent on learning tasks can be considered as unreliable, as a student may spend a long time on some activity precisely because he is not making much effort. Grades given by teachers (and even by students themselves) are time consuming, and cannot be automated.

Other approaches are related to the exploitation of behavioral data. These include the work of [START_REF] Scariot | Students Effort vs. Outcome: Analysis Through Moodle Logs[END_REF], who proposed the modeling of students' effort using Moodle's log data as a behavioral measure. Their assumption was that greater students' participation on Moodle means greater students' effort. This assumption makes sense, since having a good attendance, delivering learning tasks on time (or not), and other actions (Carbonaro, 2005), are good attitudes expected from students. Another related study is the one from [START_REF] Huptych | Measures for recommendations based on past students' activity[END_REF] which uses the total number of clicks given by a student in each activity to measure the effort. One downside of this approach is that they are only able to measure students' effort on activities that require students' to interact by clicking.

In this paper, our aim is to continue this last line of research and to propose a model that exploits behavioral data to quantify students' effort. We rely on the Cognitive Load Theory and on its methods for measuring the cognitive load. More precisely, we study the ability of different behavioral measurements to measure the effort, and propose different combination approaches to enhance the accuracy of the measurements, while being applicable to different types of learning activities.

The reminder of this paper is as follows: Section 2 describe the Cognitive Load Theory and some approaches for measuring cognitive load. Section 3 describes the dataset we collected and Section 4 shows our results using this dataset. Finally, Section 5 closes the paper.

THE COGNITIVE LOAD THEORY

The Cognitive Load Theory (CLT) was proposed by [START_REF] Sweller | Cognitive load during problem solving: Effects on learning[END_REF]. According to this theory, learning is the development and automation of schemas in the working memory and the storage of those schemas in the long-term memory for easy access and use [START_REF] Paas | Cognitive Load Measurement as a Means to Advance Cognitive Load Theory[END_REF][START_REF] Leppink | Cognitive load theory: Practical implications and an important challenge[END_REF]. The theory states that the learning design must take into account the limitations of the working memory in order to avoid underload and overload, allowing the storage of the learning schemas [START_REF] Leppink | Cognitive load theory: Practical implications and an important challenge[END_REF]. In case of underload, i.e., if the student does not exert the proper amount of effort, no new information will be stored in the long-term memory. On the other hand, in case of overload, i.e., if the student exerts a great amount of effort, there will be no cognitive resources left to store new information in the long-term memory. Overload typically happens when a task is too hard for a given student. For instance, the task may require too much knowledge in order to be completed. Processes that do not allow the creation of learning schemas may also consume the available cognitive resources, e.g., when a student divides his attention between different information sources in different spaces or times.

Many researchers consider the cognitive load as a form of student effort [START_REF] Paas | The efficiency of instructional conditions: An approach to combine mental effort and performance measures[END_REF][START_REF] Paas | Cognitive Load Measurement as a Means to Advance Cognitive Load Theory[END_REF][START_REF] Leppink | Cognitive load theory: Practical implications and an important challenge[END_REF]. Moreover, the CLT gained lots of attention since it was first proposed, becoming a consolidated research field. One goal of this field is to accurately measure the cognitive load. Although it cannot be measured directly, it can be inferred through other measures that are believed to have a high correlation with it [START_REF] Xie | Prediction of Mental Workload in Single and Multiple Tasks Environments[END_REF]. Those measures can be classified in four categories: subjective, performance, physiological and behavioral measures [START_REF] Chen | Robust Multimodal Cognitive Load Measurement[END_REF].

Subjective measures are a popular way of measuring the cognitive load [START_REF] Paas | Cognitive Load Measurement as a Means to Advance Cognitive Load Theory[END_REF][START_REF] Shi | Galvanic skin response (GSR) as an index of cognitive load[END_REF]. This approach is based on the assumption that people are capable to introspect their cognitive processes and report the mental effort exerted [START_REF] Leppink | Cognitive load theory: Practical implications and an important challenge[END_REF]. It consists in asking the participants to self-assess their cognitive load in the middle of a task [START_REF] Shi | Galvanic skin response (GSR) as an index of cognitive load[END_REF] or immediately after the task is over [START_REF] Chen | Robust Multimodal Cognitive Load Measurement[END_REF], being unsuitable for applications that require real-time data. This approach has been shown to be sensitive to small differences, valid, reliable and unobtrusive ( Paas et al., 1994[START_REF] Paas | Cognitive Load Measurement as a Means to Advance Cognitive Load Theory[END_REF], and is often used as a baseline to measure the correlation of other measures with the cognitive load [START_REF] Chen | Robust Multimodal Cognitive Load Measurement[END_REF].

Performance measures are based on the assumption that the experienced cognitive load will reflect on task outcomes, and correspond to grades, the number of correct exercises, etc. Although in the educational context it is often assumed that the more effort students exert on their learning task, the higher their outcomes will be, it is possible for two students to achieve the same outcome for a given task and exert different levels of effort on it [START_REF] Paas | Cognitive Load Measurement as a Means to Advance Cognitive Load Theory[END_REF]. This can be explained by the potential differences in previous knowledge of the students [START_REF] Hau | Prediction of academic performance among Chinese students: Effort can compensate for lack of ability[END_REF]. Thus, [START_REF] Paas | The efficiency of instructional conditions: An approach to combine mental effort and performance measures[END_REF] argue that performance measures should be combined with other types of cognitive load measures to assess the efficiency of the instructional design.

Physiological measures are based on the assumption that the increase of the experienced cognitive load leads to physiological changes [START_REF] Paas | Cognitive Load Measurement as a Means to Advance Cognitive Load Theory[END_REF]. These changes affect various body properties, such as temperature, heartbeat, pupil dilation, brain waves, etc. [START_REF] Kramer | Physiological Metrics of Mental Workload: A Review of Recent Progress[END_REF]. One advantage of the corresponding measures is that they can be captured at a high rate and with a high degree of sensitivity (Paas & Van Merriënboer, 1994), and can therefore capture variations of cognitive load over time. However, they typically require the use of specific technologies that can bias the learning experience.

Behavioral measures capture objectively and implicitly the subjects' actions [START_REF] Chen | Robust Multimodal Cognitive Load Measurement[END_REF]. Examples of behavioral measures include eye activity such as blink frequency, fixation frequency and fixation duration [START_REF] Beatty | Tracking, students' effort, and academic achievement[END_REF], speech features [START_REF] Khawaja | Potential speech features for cognitive load measurement[END_REF][START_REF] Yin | Automatic cognitive load detection from speech features[END_REF], linguistic features [START_REF] Khawaja | Measuring Cognitive Load Using Linguistic Features: Implications for Usability Evaluation and Adaptive Interaction Design[END_REF], mouse usage [START_REF] Arshad | Analysing mouse activity for cognitive load detection[END_REF], digital pen input [START_REF] Ruiz | Using pen input features as indices of cognitive load[END_REF][START_REF] Yu | Cognitive load evaluation of handwriting using stroke-level features[END_REF], gait patterns [START_REF] Verrel | Interacting effects of cognitive load and adult age on the regularity of whole-body motion during treadmill walking[END_REF], and head movements and mouth openness.

Usually, researchers only use these measurements to detect increases and decreases of the cognitive load, or to classify the cognitive load into categories such as low, medium and high. Another key point when measuring the cognitive load is that using several measures instead of just one in isolation usually increases the accuracy of the measurements by reducing noise and eventually overcoming the lack of data [START_REF] Mulder | Measurement and analysis methods of heart rate and respiration for use in applied environments[END_REF][START_REF] Chen | Robust Multimodal Cognitive Load Measurement[END_REF].

DATASET

Our goal in this paper is to propose an effort model based on behavioral data. In order to acquire such data, we wanted to rely on a course material that would contain various contents (text, images, graphics, etc.) and a clearly defined educational objectives. We chose the context of language learning, because this field allows to acquire knowledge and to restore it in a relatively short time, since the encoding of all aspects of the language and its restitution are mainly based on verbal short-term memory and verbal working memory [START_REF] Baddeley | Working memory: looking back and looking forward[END_REF].

In order to avoid a bias related to a mastery of the language prior to our study, we chose the Esperanto language, which is in little use and not studied at school. After a comparative study of the different Esperanto online learning sites, we selected the iKurso website 1 for its simple and complete course, accompanied by various exercises.

We recruited participants through a university mailing list. 14 French volunteers passed the test, 8 students, 1 engineer, 2 researchers, 2 PhD students, and 1 post-doctoral student. Our panel is composed of 6 women and 8 men. 7 are between 18 and 25 years old, 3 between 26 and 30 years old, 2 between 31 and 35 years old, and 2 between 36 and 40 years old. None of them knew Esperanto prior to our study (as answered in a questionnaire). In order to maximize the engagement of the participants in the tasks, we decided to set up a lottery whose outcome was dependent on the scores obtained on the final evaluation.

When each subject arrived, we briefly presented the material (an eye-tracker and a computer) and calibrated the eye tracker. The subject was then faced with an instruction page after which the site opened, and the learning phase began. Each subject had the opportunity to browse the different pages of the course with no time limitations. Once the participant was finished with the learning phase, he was directed to an evaluation questionnaire with 21 questions (11 sentences to translate and 10 multiple-choice questions), and could not return to the course. The experiment ended when the subject submitted his answers. Table 1 provides a summary of the scores obtained by the participants. During the learning phase, users' gaze data were retrieved using a Tobii X1 Light eye-tracker and the software Tobii Studio. We manually defined 336 areas of interest (AOIs) for all course elements required in the evaluation questionnaire. In total, for each subject, we extracted 18 characteristics [START_REF] Marchal | A First Step toward Recommendations Based on the Memory of Users[END_REF][START_REF] Marchal | First Attempt to Predict User Memory from Gaze Data[END_REF]: number of fixation points, cumulative duration, mean and standard deviation of fixations, cumulative length, mean and standard deviation of saccades, sum, mean, and standard deviation of the absolute and relative angles of the visual path; length of the first fixation relatively to the edge of the screen, number of dynamic AOIs obtained with the DBSCAN clustering algorithm, and entropy measures.

MODELLING STUDENTS' EFFORT

As mentioned in the previous section, none of the subjects had prior knowledge about Esperanto. We therefore assume their effort is the main factor influencing their outcome, and consider their score at the final questionnaire a reliable measure of effort in this case. In order to study how students' effort can be effectively measured and modeled using behavioral data, we now analyze the correlations of 1 https://ikurso.esperanto-france.org the different measurements available in the dataset with these scores, and rely on the Spearman's rank correlation coefficient.

Measuring the effort using raw indicators

We first focus on the correlations of the raw indicators extracted from the dataset. Specifically, we provide the values of the following indicators: time spent on task (TaskTime), total number of page views (#Hits), total number of clicks (#Clicks), total number of keystrokes (#Keystrokes), total time of fixations (FixationsTime), and total number of fixations (#Fixations). The correlations between these indicators and the global scores obtained by the participants are shown in Table 2. As can be seen, only small correlations were obtained. The strongest correlation we found is the one with the total number of page views (#Hits) with a coefficient of 0.28. Surprisingly, the weakest correlations are the eye gaze indicators (FixationsTime and #Fixations) with correlations coefficients near to zero.

Combining several interaction indicators

As mentioned previously, one means of increasing the accuracy of the measurements is to combine different measures. We thus created new indicators using the three following types of combinations:

1. Average time between actions: These combinations correspond to the total duration of the session divided by the number of occurrences of a type of action. These actions are pages views (#Hits), clicks (#Clicks) and keystrokes (#Keystrokes). We also combined all of them by adding them together (#Actions):

= ÷ # (1) = ÷ # (2) = ÷ # (3) = ÷ # (4) 2.
Weighted actions: This indicator combines three types of actions (page views, clicks and keystrokes) in a different way. The number of clicks (#Clicks) and keystrokes (#Keystrokes) are used as a means to weight the importance of the page views (#Hits)2 :

ℎ = # × (# + # + 1) (5)
3. Eye gaze: These indicators correspond to the average time (duration) of the fixations (Equation 6), and the average elapsed time between fixations (Equation 7):

= ÷ # (6) = ÷ # (7)
The correlations between the indicators described above and the global scores of the participants are presented in Table 3. Although still generally small, the resulting correlations are higher than the correlations coefficients shown in Table 2. Perhaps the most surprising outcome is the medium correlation (0.54) of the average duration of fixations (AvgTimeFixations). Moreover, the correlation for the weighted actions (WeightedActions) and for the average time between clicks (AvgTimeBetweenClicks) is 0.35, which is an improvement compared to the previous highest interaction correlation coefficient of 0.28 for the page views (#Hits).

Towards an effort model

We finally proceeded to create the effort model by choosing one interaction and one eye gaze indicator to combine, expecting them to be complementary and therefore able to increase the correlation with the scores when combined. Beside the average time between fixations, two previous interaction indicators had the same highest correlation values (highlighted in Table 3). Of course, the chosen eye gaze indicator is the average duration of fixations (AvgTimeFixations) as it is the highest correlation (also highlighted in Table 3).

Both types of indicators have different ranges and distributions. Thus, before combining these indicators, we normalized them by using an exponential function with and upper limit of one (Equation 8). We then combined the interaction indicators (AvgTimeBetweenClicks and WeightedActions) and the eye gaze indicator (AvgTimeFixations) into the model as shown in Equation 93 .

( ) = 1 - (8) = × ( ( ℎ )) + × ( ( )) (9)
The correlations results for these combinations are shown in Table 4. As can be seen, the highest correlation is 0.59 for the combination of WeightedActions (w1 = 0.7) with AvgTimeFixations (w2 = 0.3). Overall, we were thus able to increase the correlation by more than 100% compared to the initial correlations.

The other combination (AvgTimeBetweenClicks and AvgTimeFixations) did not improve the correlation (i.e., the highest correlation still equal to the correlation of the eye gaze indicator alone), which suggests that the average time between clicks, which is not as flexible to the type of task as the WeightedActions indicator, is not complementary to the eye gaze indicator. This is not surprising, as people usually watch the screen when using the mouse.

Table 4. Comparison of the combined indicators

AvgTimeBetweenClicks and AvgTimeFixations 0.54 WeightedActions and AvgTimeFixations 0.59

CONCLUSION

A number of definitions have been proposed for the concept of students' effort. Usually, these definitions are related to various students' behaviors such as attending classes, delivering assignments on time, participating in class, etc. The Cognitive Load Theory allows to understand the effort as the cognitive load experienced by students. The theory also explains that learning occurs when we create and automate schemas in the working memory and then store them in the long-term memory, stating that the limitations of the working memory should be respected in order to allow learning.

This theory gained lots of attention and several researchers are now looking for new and more effective ways of measuring the imposed cognitive load (i.e., effort) in order to detect and avoid underload and overload. Different means of acquiring measurements of the cognitive load exist, and they can be classified into subjective, performance, physiological and behavioral measures. However, those measurements only allow to classify or identify an increase or decrease in the cognitive load.

In this paper, we proposed a new model that allows to quantify students' effort, as opposed to identified or classified as shown in the cognitive load research. Despite the limitations of our dataset (i.e., absence of effort ratings and number of subjects) and the need of further investigation, our study adopts some new approaches that can offer a better understanding of students' effort. First, it relies on the Cognitive Load Theory that explains how learning occurs, the limitations that should be considered while designing learning activities (i.e., the working memory has a limit that should be respected), and also the role of effort in achieving learning outcomes. Second, it uses interaction and eye gaze data which can reduce noise and account for missing data [START_REF] Mulder | Measurement and analysis methods of heart rate and respiration for use in applied environments[END_REF][START_REF] Chen | Robust Multimodal Cognitive Load Measurement[END_REF]. Third, the model can still be used if only part of the data is available, even though it would result in a smaller correlation (e.g., if only the interaction data are available, the correlation coefficient would be 0.35 instead of 0.59).

Our results show that our approach is able to provide measurements that have a medium correlation with effort. Especially, our proposed combination increased the correlation score by more than 100% compared to raw indicators. This approach can be exploited to develop effort-based educational tools and help both teacher and students. For instance, with proper dashboards, teachers could be able to identify students who are not well engaged into learning (i.e., not exerting enough effort on their learning tasks) and students who are struggling (i.e., exerting too much effort on their learning tasks, possibly meaning that they lack previous knowledge to handle the proposed tasks). Similarly, students could identify if they are just not engaged enough or if they are struggling with the proposed learning tasks, leading them to seek help from their teachers and classmates. The proposed model can also be used in fully automated tools. For instance, recommendation systems could identify how much effort a student should exert in a given moment and recommend the ideal learning tasks, with the goal of promoting his engagement.

In the future, we intend to create a new dataset and run the model to see how it performs and how it can be further enhanced. Later, we want to add new behavioral (e.g., movements) and physiological measurements (e.g., pupil dilation, and skin temperature). Our ultimate goal is to be able to exploit our effort model to provide engaging recommendations to the students.

Table 1 : Summary of users' scores on the evaluation questionnaire

 1

		Grammar score (/11)	Vocabulary score (/11)	Translation score (/11)	MCQ (/10)	Global score
	Mean	4.28	2.92	1.92	8.78	10.23
	Median	3.50	2.50	1.00	9.00	10.00
	Standard deviation	3.66	2.33	2.58	1.42	3.53

Table 2 : Raw indicators correlation with scores

 2

	Type	Indicator	Correlation Level
	Interaction TaskTime	0.21 Low
		#Hits	0.28 Low *
		#Clicks	0.14 Low
		#Keystrokes	0.10 Low
	Eye gaze	FixationsTime	-0.08 Low *
		#Fixations	0.00 Low *

Table 3 : Combined indicators correlation with scores

 3

	Type	Indicator	Correlation Level
	Interaction AvgTimeBetweenHits	0.05 Low
		AvgTimeBetweenClicks	0.35 Low	*
		AvgTimeBetweenKeystrokes	0 Low
		AvgTimeBetweenActions	-0.18 Low
		WeightedActions	0.35 Low	*
	Eye gaze	AvgTimeBetweenFixations	0.36 Low
		AvgTimeFixations	0.54 Medium *

This equation contains an addition of one to avoid having a value of zero when the task does not require any clicks or keystrokes to be completed (e.g., reading a text).

We empirically determined the value of the parameters that led to the higher correlation coefficients. We did however not systematically optimize these values.


Manon Marchand

Frédéric Restagno

Emmanuelle Rio

François Boulogne

Roughness-induced friction in liquid foams

Complex liquids flow is known to be drastically affected by the roughness condition at the interfaces. We combined stresses measurements and observations of the flow during the motion of different rough surfaces in dry liquid foams. We visually show that three distinct friction regimes exists: slippage, stick-slip motion, and anchored soap films. Our stress measurements are validated for slippage and anchored regimes based on existing models, and we propose a leverage rule to describe the stresses during the stick-slip regime. We find that the occurrence of the stick-slip or anchored regimes is controlled by the roughness factor, defined as the ratio between the size of the surface asperities and the radius of curvature of the Plateau borders.

The flow of complex fluids -polymers [START_REF] Priestley | Structural relaxation of polymer glasses at surfaces, interfaces, and in between[END_REF][START_REF] Boukany | Molecular imaging of slip in entangled dna solution[END_REF], emulsions [START_REF] Goyon | Spatial cooperativity in soft glassy flows[END_REF], granular materials [START_REF] Siavoshi | Friction of a slider on a granular layer: Nonmonotonic thickness dependence and effect of boundary conditions[END_REF][START_REF] Pouliquen | On the shape of granular fronts down rough inclined planes[END_REF], bubbly liquids [START_REF] Germain | Bubbles slipping along a crenelated wall[END_REF], foams [START_REF] Kabla | Local stress relaxation and shear banding in a dry foam under shear[END_REF][START_REF] Golemanov | Breakup of bubbles and drops in steadily sheared foams and concentrated emulsions[END_REF] near a solid surface displays different behaviors depending on the surface properties. Often, these systems exhibit a slippage on smooth surfaces but deform and flow on rough surfaces. Therefore, asperities are commonly added on the measurement apparatus to suppress the interfacial dissipations [START_REF] Barnes | A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: its cause, character, and cure[END_REF][START_REF] Cloitre | A review on wall slip in high solid dispersions[END_REF][START_REF] Cohen-Addad | Flow in foams and flowing foams[END_REF]. Here, we focus our study on the flow of foams for which the elementary elements, the bubbles, can be observed directly.

The friction of an elongated bubble in a smooth round capillary has been studied in the pioneering work of Bretherton at low capillary numbers Ca = µV /γ, where µ and γ are the dynamic viscosity and air-liquid surface tension of the solution, and V is the meniscus velocity in the capillary [START_REF] Bretherton | The motion of long bubbles in tubes[END_REF]. It is shown experimentally and theoretically that the stress follows a Ca 2/3 power law. This prediction is also valid for a single bubble in a flat cell [START_REF] Park | Two-phase displacement in hele shaw cells: theory[END_REF], and can be extended for foams [START_REF] Cantat | Liquid meniscus friction on a wet plate: Bubbles, lamellae, and foams[END_REF]. The surface rheology of the foaming solution influences the power law, but in this study we work with a solution for which this issue is negligible [START_REF] Cantat | Liquid meniscus friction on a wet plate: Bubbles, lamellae, and foams[END_REF][START_REF] Denkov | Wall slip and viscous dissipation in sheared foams: Effect of surface mobility[END_REF]. Also, experimental measurements provide a correction accounting for the liquid fraction of the foam ϕ [START_REF] Raufaste | Dissipation in quasi-two-dimensional flowing foams[END_REF].

In rheology, the wall slippage of the probed material must be avoided to ensure that the dissipation is localized in the bulk of the sample. In the case of foams, a commonly adopted rule-of-thumb to prevent slippage consists in adding asperities larger than the bubble size on the walls [START_REF] Khan | Foam rheology: III. measurement of shear flow properties[END_REF], and to assert either visually [START_REF] Katgert | Couette flow of two-dimensional foams[END_REF] or by showing that the rheological measurements do not depend on the confinement [START_REF] Denkov | Wall slip and viscous dissipation in sheared foams: Effect of surface mobility[END_REF][START_REF] Cloitre | A review on wall slip in high solid dispersions[END_REF], that there is no remaining slippage. This trial and error process is not always possible and the characterization of the effect of different roughness sizes has been studied for single wet bubbles on walls [START_REF] Germain | Bubbles slipping along a crenelated wall[END_REF], but not for dry liquid foams.

In this Letter, we explore systematically the effect of different sizes of wall asperities a on the flow of dry liquid foams and we identify three friction regimes at zero, high or intermediate roughness. The contribution of the roughness size a, of the liquid fraction ϕ , and of the inserting velocity in the foam V to the stresses are rationalized in each regime. The roughness size is shown to change the stresses over one order of magnitude. We show that the roughness factor a/r pb is a single criterion for the crossover between wall and bulk dissi-pation regimes. Interestingly, this parameter is independent of the imposed velocity.

Our experiment consists in inserting horizontally a controlled rough surface in a dry monodisperse foam generated in a transparent container (Fig. 1a andb). We produce the foam by blowing air through needles in a foaming solution. The obtained bubble radius is R = 0.70 ± 0.05 mm, and the liquid fraction ϕ of the foam can be varied between 0.03 and 8 % by changing the working height above the liquid-foam interface [START_REF] Maestro | Liquid dispersions under gravity: volume fraction profile and osmotic pressure[END_REF] (Fig. S2). For such dry foams, the radius of curvature of the Plateau borders is given by r pb = R ϕ /0.33 [START_REF] Koehler | A generalized view of foam drainage: Experiment and theory[END_REF]. It varies in the range 0.02 -0.4 mm in our experiment. Model rough surfaces are obtained by gluing glass beads of mean radii a on microscope glass slides (Fig. S1), Fig. 1a). We insert the surfaces in foams at constant velocities V from 0.5 to 20 mm/s, corresponding to capillary numbers Ca in the range 1.7 × 10 -5 to 6.7 × 10 -4 . Simultaneously, we measure the tangential force F exerted by the foam on the surface (Fig. S3).

By tracking the position of the Plateau borders p pb in contact with the patterned surface during the motion, we identify three distinct friction regimes (Fig. 1d), which are discriminated by the dimensionless roughness factor a/r pb . The emergence of this parameter can be intuited. When a bead is smaller than the size of the Plateau border r pb , it enters the Plateau border and slides inside it whereas bigger beads experience a pinning force at the liquid air interface (Fig. 2e). For negligible roughness sizes compared to the characteristic size of a Plateau border, a r pb , the Plateau borders slide on the solid surface (Supplementary Movie S1). For a ∼ r pb , Plateau borders are anchored on the surfaces but occasionally jump back (Supplementary Movie S2), while for a r pb Plateau borders remain anchored and the stress is released by plastic events between bubbles in the bulk of the foam (Fig. 1d, e, Supplementary Movie S3). We will respectively refer to these regimes as sliding, stick-slip, and anchored regimes in the following discussion. For a/r pb between 1 and 3, the visualizations reveal that the stress is released by mixed slip or plastic events. This provides a first estimate of the transition between the stick-slip regime and the anchored one.

Typical force measurements as a function of time t, or equivalently of the position of the surface p, are presented for each regime in Fig. 1c. The linear evolution of the force indicates that the probed phenomena are independent of the penetration depth of the surface, and that a constant stress value τp can be extracted from F (t) and p(t) for each experiment (Fig. S5). We reproduce the experiment for various roughness sizes a, radius of curvature of Plateau borders r pb , and insertion velocities V . In Fig. 2a, we plot the stress τp as a function of the roughness factor a/r pb . The different point colors represent the three regimes identified from the images. In this representation, the data for a single velocity collapses on a trend curve (Fig. S4). Complementary representations of the stick-slip and the anchored regimes presenting the influence of the asperity size a and the velocity V are provided in Fig. S7. Interestingly, tuning a/r pb leads to a stress variation of about an order of magnitude, which highlights the crucial effect of the boundary conditions on stresses. In the following, we examine each regime to rationalize the dynamics.

The sliding regime, for which a r pb , has already been investigated [START_REF] Bretherton | The motion of long bubbles in tubes[END_REF][START_REF] Raufaste | Dissipation in quasi-two-dimensional flowing foams[END_REF][START_REF] Cantat | Liquid meniscus friction on a wet plate: Bubbles, lamellae, and foams[END_REF], and these studies validate experimentally that the stress at the solid wall can be written

τ slip = 3.8 γ R ϕ -0.25 Ca 2/3 . (1)
In Fig. 2b, the stress measurements are plotted as a function of the prediction given by equation ( 1), which shows a good agreement and validates this experimental approach. Now, we consider the anchored regime for the large roughness factors. The common description of the foam rheology suggests that for shear stresses lower than a yield stress τys, the foam behaves as an elastic solid, whereas for stresses exceeding the yield stress, the foam flows. Phenomenologically, this behavior is described by a Hershell-Bulkley law τHB = τys + η( γ) γ, where γ ∼ V /δ is the shear rate that scales as the velocity over a characteristic shear length δ and η( γ) is the effective foam viscosity that depends on γ [START_REF] Denkov | The role of surfactant type and bubble surface mobility in foam rheology[END_REF][START_REF] Cohen-Addad | Flow in foams and flowing foams[END_REF]. The ratio of the yield stress and the viscous term defines the Bingham number Bi = τys η( γ) γ [START_REF] Bingham | An investigation of the law of plastic flow[END_REF]. The yield stress value is described by a semi-empirical law τys = K γ R (ϕc -ϕ ) 2 , where ϕc = 0.26 is the fraction of gaps remaining in a close-packing of hard spheres [START_REF] Maestro | Liquid dispersions under gravity: volume fraction profile and osmotic pressure[END_REF], and K is a proportionality factor which reported values vary between 0.5 and 6 [START_REF] Lexis | Yield stress and elasticity of aqueous foams from protein and surfactant solutions -the role of continuous phase viscosity and interfacial properties[END_REF][START_REF] Rouyer | Is the yield stress of aqueous foam a well-defined quantity? Colloids and Surfaces A[END_REF]. Since we are working with dry foams, we have ϕ ϕc, which leads to

τys = K γ R ϕ 2 c . (2)
In the limit of low velocities, corresponding to Bi > 1, the contribution of the yield stress is dominant (see SI). The Fig. 2d shows that the stress applied by the foam on the rough surfaces is nearly independent on the velocity and its value is predicted by the equation ( 2) with a prefactor K = 2.9 ± 0.3, which is in agreement with previously recorded values [START_REF] Lexis | Yield stress and elasticity of aqueous foams from protein and surfactant solutions -the role of continuous phase viscosity and interfacial properties[END_REF][START_REF] Rouyer | Is the yield stress of aqueous foam a well-defined quantity? Colloids and Surfaces A[END_REF]. We notice that the measured stress increases slightly for the larger velocities, which is reminiscent of the viscous term in the Hershell-Bulkley model.

Up to this point, we analyzed the two extreme limits of negligible and large dimensionless roughness factor a/r pb . For roughness sizes comparable to the radius of the Plateau borders, we observe a stick-slip regime that has been observed but not characterized [START_REF] Buchgraber | Microvisual investigation of foam flow in ideal fractures: Role of fracture aperture and surface roughness[END_REF], to the best of our knowledge. Our experiments indicate that the transition between the stickslip and the anchored regimes is continuous (Fig. 2a). This suggests that the stick-slip regime is a combination of sliding, where the energy is released by viscous dissipation in the Plateau borders, and anchoring, where the energy is stored by deforming elastically the foam.

In the stick-slip regime, (Fig. 2e) an asperity moving in a foam goes through the liquid air interface of a Plateau border over a duration t anchored ∝ a/V , experiencing a pinning force. Then, the asperity moves inside the Plateau border over a typical duration t slip ∝ r pb /V . Therefore, we introduce the ratio of these durations, ã = a/kr pb , where the prefactor k represents the value of the transition. This two-step description happens for each asperity on the whole probing surface. The stick-slip events are not occurring simultaneously (Supplementary Movie S2), thus we average the individual behaviors of the Plateau borders. Hence, we construct a leverage rule stating that the total stress is the sum of the contributions of a pinning stress for a relative duration ã and of a viscous stress for the complementary relative duration (1 -ã). This writes

τ stick-slip = τysã + τ slip (1 -ã). (3)
To determine more precisely the value of the transition k, we optimized equation ( 3) against this parameter and we obtained a transition at k = 1.9 ± 0.2 (Fig. S6a). This value of

s l i d i n g a n c h or ed (a) (b) (c) (d) (e)
stick -s lip 3) for V → 0, and the dashed black line is τys with K = 2.9. The gray area shows the transition between the stick-slip and the anchored regime as deduced from observation of the videos, and the orange area is the transition obtained by optimizing k in Eq. ( 3). (b) For a/r pb = 0, stress measurements as a function of the equation ( 1). (c) Stress values for the sliding (green circles) and the stick-slip (blue triangles) conditions, as a function of equation ( 3). (d) In the anchored regime, measured stresses as a function of the imposed velocity V . The solid line is the mean of all stresses τys and the gray area represents the standard deviation. The deviation for the higher velocities indicates a more significant contribution of the viscous term in the Hershell-Bulkley model. (e) Schematics of a Plateau border moving on a rough surface. The beads spend a time proportional to a/V going through the liquid air interface, and a time proportional to r pb /V in the bulk of the Plateau border.

order unity is in agreement with our estimation of the transition from direct visualizations of the Plateau border dynamics (see the orange and gray areas in Fig. 2a). As shown in Fig. 2c, the proposed equation ( 3) is in excellent agreement with the stress measurements for the different liquid fractions and surface velocities explored in this study. In the vicinity of small velocities, we expect τ stick-slip → V →0 τysã, and this is observed in Fig. 2a and Fig. S6b.

Thus, we identified a practical criterion ã to discriminate between surface and bulk dissipation for the friction of a foam on a solid surface. The anchored regime is of particular interest for rheological studies focusing on the flow of foams where a no slip condition is necessary to transfer shear to the bulk of the material. It was already known that adding some asperities by gluing sand paper or engraving grooves on a measuring apparatus reduces the wall slippage [START_REF] Khan | Foam rheology: III. measurement of shear flow properties[END_REF], but the size of these asperities had not been tuned systematically. Our study validates this approach, since the stress in the anchored regime are independent of the size of the asperities beyond a critical roughness factor (Fig. 2a). When the grit size of the sand paper is insufficient to totally eliminate the wall slippage, the mixed surface and bulk dissipation leads to a difficult interpretation of the data [START_REF] Golemanov | Breakup of bubbles and drops in steadily sheared foams and concentrated emulsions[END_REF]. Differences in the measured stresses are also reported when the grit size is increased [START_REF] Jimenez-Junca | Rheology of milk foams produced by steam injection[END_REF]. This behavior is likely the stick-slip regime we report in Fig. 2c. Our contribution allows one to choose a suitable roughness to be added on the measuring systems regarding the foam properties. The results then assess that the obtained measurements in the anchored regime will be uncorrelated with the size of the roughness.

The stick-slip regime allows, for instance, to understand the mastication of an aerated food (Fig. 3a). Adding air bubbles in a food product affects mouthfeel perception, improves digestibility, and aids mastication [START_REF] Campbell | Creation and characterisation of aerated food products[END_REF]. In the case of eating disorders, such as dysphagia, more viscous foods are proven to be safer [START_REF] Nishinari | Role of fluid cohesiveness in safe swallowing[END_REF]. With viscosities typically 10 3 times bigger than the viscosity of water [START_REF] Marze | Protein and surfactant foams: linear rheology and dilatancy effect[END_REF], foams could help patients. We make a visualization experiment to illustrate the tunability of perception during the mastication of a foamed food. Human tongue asperities have a fixed size, therefore the remaining adjustable parameters in this case are the bubble size and the liquid fraction of the foam. A glass slide covered with asperities of mean radius a = 225 µm, a size comparable to human papillae [START_REF] Essick | Lingual tactile acuity, taste perception, and the density and diameter of fungiform papillae in female subjects[END_REF], can be considered as a model human tongue (Fig. 3a, b andc). We produce two edible albumen foams with a bubble size R = 0.7 mm and two different liquid fractions, using the same technique than soap foams, but with a solution containing 1 g of egg white powder (Louis François) and 200 mL of deionized water. The two foams are sheared between a table spoon moving at 10 mm/s and the static model tongue. In the two cases, the last bubble is circled to illustrate the slippage of the foam (Fig. 3d). For the wetter foam for which ã 0.5 < 1, the conditions predict a stick-slip regime and the foam moves on the surface (Supplementary Movie S4), whereas for the dryer foam, for which ã 3 > 1, the foam sticks to the surface (Supplementary Movie S5). This illustrates that the results of our controlled experiment are valid in a more general context, with different shearing geometries and surfactants. When the normalized roughness ã varies from 0 to 1 in the stick-slip regime, we see in Fig. 2a that the stress varies between 0.8 and 9.8 Pa, a range of stresses detectable by a human tongue [START_REF] Foegeding | Transforming structural breakdown into sensory perception of texture[END_REF][START_REF] Linne | Quantification of oral roughness perception and comparison with mechanism of astringency perception[END_REF]. Thus, tuning the macroscopic properties of a product, namely the bubble size and the liquid-gas ratio, must lead to different sensations in mouth.

In conclusion, we reveal that the foam flow near surfaces exhibit different behaviors: sliding, anchored, and stick-slip. By recording the stresses exerted during these regimes, we show that there exists a roughness, normalized by the curvature radius of the Plateau borders of the foam, ã = a/kr pb beyond which the dissipation is transferred from the surface to the bulk. This transition does not depend on the imposed velocity in the explored range. In the stick slip regime, we propose a leverage rule describing the influence of speed, radius of curvature of Plateau borders, and liquid fraction on the stresses exerted on the walls. We measure that these stresses vary on one order of magnitude when the normalized roughness is increased. Therefore, we contribute to an improved description of wall roughness effect on flowing foams, which is of particular interest to design surfaces given the foam properties in industrial applications. In contrast, when surface asperities are unchangeable, as in the case of tongue papillae, our description of friction forces allows to finely tune the properties of edible foams to get creamy or gooey mouth feelings. This is useful for inventing new foamed food products, either for the ease of feeding for dysphagic patients, or for the gourmets' pleasure.

Figure 1 :

 1 Figure 1: Foam flow dynamics near a solid surface decorated with glass beads. (a) Side view of the surface of roughness size a moving at constant speed V in a foam of bubble radius R and radius of curvature of Plateau borders r pb . The force F exerted by the foam on the surface is recorded. (b) Photograph corresponding to the schematic (a). The scale bar is 5 mm. (c) Raw force measurements as a function of time t and position of the surface p for one smooth and two patterned surfaces translating at V = 1 mm/s from left to right. (d) Visualization of the Plateau borders in contact with the patterned surfaces for three different a/r pb . The bottom of each picture is the surface moving at 1 mm/s. We mark the position p pb of a Plateau border with a circle. A plastic event is circled in white. The scale bar represents 2 mm. (e) Position of the Plateau borders p pb for the three friction regimes, reported from (d).

Figure 2 :

 2 Figure 2: Stress measurements and identification of the three friction regimes. (a) Stress τp obtained from the force measurements as a function of the roughness factor a/r pb . The solid black line represents the equation (3) for V → 0, and the dashed black line is τys with K = 2.9. The gray area shows the transition between the stick-slip and the anchored regime as deduced from observation of the videos, and the orange area is the transition obtained by optimizing k in Eq. (3). (b) For a/r pb = 0, stress measurements as a function of the equation (1). (c) Stress values for the sliding (green circles) and the stick-slip (blue triangles) conditions, as a function of equation (3). (d) In the anchored regime, measured stresses as a function of the imposed velocity V . The solid line is the mean of all stresses τys and the gray area represents the standard deviation. The deviation for the higher velocities indicates a more significant contribution of the viscous term in the Hershell-Bulkley model. (e) Schematics of a Plateau border moving on a rough surface. The beads spend a time proportional to a/V going through the liquid air interface, and a time proportional to r pb /V in the bulk of the Plateau border.

Figure 3 :

 3 Figure 3: Edible foams and texture sensation. (a) Albumen foam in a spoon. The scale bar is 1 cm. A drop of food dye is added for visualization. (b) Rough surface with beads of mean radius a = 225 µm. The scale bar is 5 mm. (c) Close up picture that shows the papillae on a human tongue. The scale bar is 5 mm. (d)Albumen foam sheared between a table spoon and a glass surface covered with beads of mean radius a = 225 µm. The left side is a wet foam with ϕ 0.7 %, corresponding to ã 0.5. The right side is a dryer foam with a liquid fraction ϕ 0.02 %, meaning ã 3. In those two cases the last bubble on the surface is circled to enlighten the motion of foam on the model tongue. There is a 1 s interval between two consecutive images. The scale bar is 1 cm.

Acknowledgements M.M. acknowledges EDPIF for funding support. We thank J. Sanchez for programming the computer interface of the experiment, and G. Guillier for support manufacturing the force sensor. We thank B. Dollet and C. Raufaste for discussions.