Quentin Villermet
email: roth@cmb.hu-berlin.de

Follow the guides: disentangling human and algorithmic curation in online music consumption

Keywords: CCS Concepts:, Human-centered computing → Empirical studies in HCI, • Information systems → Multimedia streaming, Recommender systems

The role of recommendation systems in the diversity of content consumption on platforms is a much-debated issue. The quantitative state of the art often overlooks the existence of individual attitudes toward guidance, and eventually of different categories of users in this regard. Focusing on the case of music streaming, we analyze the complete listening history of about 9k users over one year and demonstrate that there is no blanket answer to the intertwinement of recommendation use and consumption diversity: it depends on users. First we compute for each user the relative importance of different access modes within their listening history, introducing a trichotomy distinguishing so-called 'organic' use from algorithmic and editorial guidance. We thereby identify four categories of users.

We then focus on two scales related to content diversity, both in terms of dispersion -how much users consume the same content repeatedly -and popularity -how popular is the content they consume. We show that the two types of recommendation offered by music platforms -algorithmic and editorial -may drive the consumption of more or less diverse content in opposite directions, depending also strongly on the type of users. Finally, we compare users' streaming histories with the music programming of a selection of popular French radio stations during the same period. While radio programs are usually more tilted toward repetition than users' listening histories, they often program more songs from less popular artists. On the whole, our results highlight the nontrivial effects of platform-mediated recommendation on consumption, and lead us to speak of 'filter niches' rather than 'filter bubbles'. They hint at further ramifications for the study and design of recommendation systems.

INTRODUCTION

The contribution of algorithmic guidance to user preferences and behavior is at the heart of an active debate backed by an increasing number of empirical studies. This literature typically relies on some notion and measure of diversity, and on some dichotomy between user activity with and without recommendation. The latter, diversely denoted as "organic", "autonomous", "self-selected" behavior, generally serves as a reference point of what users would do had they not been advised or even diverted by algorithms. Nevertheless, many studies focused on user practices have emphasized how user navigation may both passively and actively rely on recommendation devices. The concept of "navigational queries" [START_REF] Broder | A taxonomy of web search[END_REF] first described how search engines may be used to access content that one is already aware of, and where, for instance, autocompletion suggestions merely play a limited role, essentially by reading the user's mind and accelerating their navigation [START_REF] Bhaskar Mitra | On User Interactions with Query Auto-Completion[END_REF]. Beyond this simple old case, a growing literature points at the diversity of user practices and expectations toward platform-based recommendation; in the context of music streaming platforms, see [START_REF] Beuscart | Music recommendation algorithms and listener autonomy -The listening patterns of a panel of music streaming users[END_REF][START_REF] Karakayali | Recommendation systems as technologies of the self: Algorithmic control and the formation of music taste[END_REF][START_REF] Webster | Taste in the platform age: Music streaming services and new forms of class distinction[END_REF]. Recommendation most likely does not apply similarly on all users. In other words, its influence should be studied by differentiating user classes who distinctly rely on, and plausibly respond to, recommendation. This issue should furthermore be framed within a broader context where guidance may stem both from algorithmic devices and from human recommendations. The latter is arguably not new: friends and relatives, mainstream media and salesclerks have traditionally played a prime role in suggesting and shaping consumption preferences. In the music realm, the composition of radio playlists has typically long been decided by humans. The flourishing development of human-mediated, or "editorial", guidance [START_REF] Bandy | Auditing news curation systems: A case study examining algorithmic and editorial logic in Apple News[END_REF][START_REF] Bonini | First Week Is Editorial, Second Week Is Algorithmic": Platform Gatekeepers and the Platformization of Music Curation[END_REF] may however sometimes appear as a blind spot in the appraisal of platform-based recommendation. Building upon this recent trend, we extend the usual algorithmic/organic dichotomy by considering editorial guidance as a specific, distinct mode of recommendation. Contemporary music streaming platforms epitomize this trichotomy for they feature the three types of access to content: algorithmic (songs suggested by a recommendation engine, for instance in autoplay mode), editorial (songs curated by the platform staff, for instance as "featured playlists") and organic (self-selected songs, either from personal playlists and favorite albums, or directly sought through the search bar). Note that in all three cases, it is obviously the user who chooses the mode of access: what matters in this trichotomy is that song titles are proposed by an algorithm, the editorial staff, or the user themselves.

The case of music streaming further makes it empirically feasible to connect the role of platform-based recommendation with traditional content curation. Specifically, we are able to contrast listening practices of users who rely more or less on some types of platform recommendation affordances with the mass (and somewhat traditional) guidance proposed by music radios, as an offline or "off-platform" reference point. Our study is thus based on two datasets: first, anonymized yet comprehensive listening histories for several thousands of users active on a major music streaming platform over a certain period of time. Second, playlists for a selection of mainstream radios in France over the same period.

On the whole, we aim to concretely examine (i) whether there exists distinct behavioral patterns with respect to the three modes of access to content and (ii) whether some type of guidance tends to pull listeners towards exploring certain types of content. We characterize the exploratory nature of listening histories with two distinct notions, dispersion and artist popularity, which correspond to two dimensions of diversity -i.e., dispersion at the user level (skewed popularity of content within a given user's listening portfolio: redundancy or not) and dispersion at the macro level (skewed popularity of artists over all users: mainstream or not).

The main contributions are as follows:

• we hypothesize the existence of distinct classes of user attitudes towards recommendation before examining its possible influence on content consumption patterns;

• we further differentiate between two types of platform-side recommendation, stemming either fully from algorithmic suggestions or primarily from human curation;

• we establish a bridge between online platform recommendation and one of the traditional types of music guidance from the non-platform world, exemplified by radio music playlists.

RELATED WORK

Diversity and recommendation systems. The role of recommendation devices in fostering diversity is assuredly at the heart of a fast-growing literature focused on a myriad of platform types, where music streaming is only one application case among many. Contrarily to popular assumptions about so-called "filter bubbles", the emerging empirical picture suggests that recommendation algorithms generally seem to increase diversity and serendipity [START_REF] Luca | Evolution of Ego-networks in Social Media with Link Recommendations[END_REF][START_REF] Bakshy | Exposure to ideologically diverse news and opinion on Facebook[END_REF][START_REF] Haim | Burst of the Filter Bubble? Effects of personalization on the diversity of Google News[END_REF][START_REF] Möller | Do not blame it on the algorithm: an empirical assessment of multiple recommender systems and their impact on content diversity[END_REF][START_REF] Puschmann | Beyond the bubble: Assessing the diversity of political search results[END_REF][START_REF] Roth | Algorithmic Distortion of Informational Landscapes[END_REF], even though recent results on specific platforms such as Spotify or YouTube tend to suggest otherwise [START_REF] Anderson | Algorithmic effects on the diversity of consumption on spotify[END_REF][START_REF] Roth | Tubes and bubbles topological confinement of YouTube recommendations[END_REF], while explicit personalization or "self-selection" also appear to induce algorithmic reinforcement and confinement, for instance regarding news consumption [START_REF] Dylko | The dark side of technology: An experimental investigation of the influence of customizability technology on online political selective exposure[END_REF][START_REF] Zuiderveen Borgesius | Should we worry about filter bubbles?[END_REF]. Most of this literature works at the aggregate level without distinguishing populations of users who may differently use or respond to algorithmic guidance. Several studies nonetheless expressly differentiate users who are eager for recommendation [START_REF] Tien T Nguyen | Exploring the filter bubble: the effect of using recommender systems on content diversity[END_REF], diversity [START_REF] Munson | Presenting Diverse Political Opinions: How and How Much[END_REF], or exploration [START_REF] Garcia-Gathright | Understanding and Evaluating User Satisfaction with Music Discovery[END_REF][START_REF] Hosey | Just Give Me What I Want: How People Use and Evaluate Music Search[END_REF]. This hints at the existence of different user behaviors and expectations towards recommendation [START_REF] Karakayali | Recommendation systems as technologies of the self: Algorithmic control and the formation of music taste[END_REF] prior to it influencing users.

Use of music streaming platforms. Music streaming platforms feature an array of recommendation uses. They may be employed as "intimate experts" [START_REF] Karakayali | Recommendation systems as technologies of the self: Algorithmic control and the formation of music taste[END_REF] who are able to counsel users in the most personalized manner and contribute to the self-formation of taste. They also provide editorial guidance which induces a hybrid type of curation, distinct from pure algorithmic recommendation [START_REF] Bonini | First Week Is Editorial, Second Week Is Algorithmic": Platform Gatekeepers and the Platformization of Music Curation[END_REF]. The co-existence of algorithmic and editorial guidance is not unique to music streaming: their differential effect has already been studied on news platforms, where editorial recommendations appear to outperform algorithms in terms of diversity or in terms of concentration [START_REF] Bandy | Auditing news curation systems: A case study examining algorithmic and editorial logic in Apple News[END_REF]. This issue connects with a relatively older literature appraising the role of online retail platforms in the consumption of content of varying popularity, especially at the top and bottom of the so-called "long tail" [START_REF] Elberse | Should you invest in the long tail?[END_REF][START_REF] Goel | Anatomy of the long tail: ordinary people with extraordinary tastes[END_REF]. Curation on music platforms also opens specific opportunities with respect to the access to niche content [START_REF] Barna | The perfect guide in a crowded musical landscape:" Online music platforms and curatorship[END_REF]. In this regard, quantitative studies show that platform use in general is associated with listening to less mainstream and less redundant content [START_REF] Datta | Changing their tune: How consumers' adoption of online streaming affects music consumption and discovery[END_REF], even though diversity seems to plateau for the most active users [START_REF] Poulain | Investigating the lack of diversity in user behavior: The case of musical content on online platforms[END_REF]. However, the proper contribution of recommendation in these aggregate studies remains difficult to assess. Two recent studies differentiate organic from guided navigation and appear to yield conflicting results, whereby the former [START_REF] Anderson | Algorithmic effects on the diversity of consumption on spotify[END_REF] or contrarily the latter [START_REF] Beuscart | Music recommendation algorithms and listener autonomy -The listening patterns of a panel of music streaming users[END_REF] is shown to be correlated with increased consumption diversity. Notwithstanding, here again, little is known on the existence of underlying types of users (or even classes of users in the sociological sense, as in [START_REF] Webster | Taste in the platform age: Music streaming services and new forms of class distinction[END_REF]) who make use of the platform affordances in different waysand, in turn, how the same affordances distinctly affect these user populations in their exploration of different regions of the musical space.

Music recommendation goals. The intertwinement between expectations, uses and influences is not foreign to the more technical issue of the design of recommendation. The introduction of recommending devices is generally posterior to the creation of music streaming platforms, which were often initially operating as pure digital libraries (a notable exception being Pandora). While recommendation may first have been construed as an "attentional trap" i.e., to help retaining the user longer on the platform [START_REF] Seaver | Captivating algorithms: Recommender systems as traps[END_REF], the question of what it aims to optimize and how it intends to improve user experience provides further context to our contribution. The work of [START_REF] Bonnin | Automated generation of music playlists: Survey and experiments[END_REF] offers a comprehensive overview of the current techniques for automated playlist creation, and their evaluation. It emphasizes in particular the importance of taking into account song popularity (e.g., to tackle the cold-start problem [START_REF] Bauer | Global and country-specific mainstreaminess measures: Definitions, analysis, and usage for improving personalized music recommendation systems[END_REF]), while radio playlists are said to typically "contain popular tracks in a relatively homogeneous style". Models that generate and rely on categories of user tastes have also been proposed [START_REF] Vigliensoni | Automatic Music Recommendation Systems: Do Demographic, Profiling, and Contextual Features Improve Their Performance?[END_REF][START_REF] Zheleva | Statistical models of music-listening sessions in social media[END_REF] and seem to go much further than the above-mentioned literature in framing algorithmic recommendation in terms of implicit user classes. Regardless, the conception of music recommendation systems already makes significant use of so-called "beyond accuracy" measures [START_REF] Sean M Mcnee | Being accurate is not enough: how accuracy metrics have hurt recommender systems[END_REF] by attempting at integrating diversity-related metrics [variously denoted as coverage, serendipity, novelty, see [START_REF] Kaminskas | Diversity, serendipity, novelty, and coverage: a survey and empirical analysis of beyond-accuracy objectives in recommender systems[END_REF][START_REF] Schedl | Current challenges and visions in music recommender systems research[END_REF][START_REF] Yuan | Auralist: introducing serendipity into music recommendation[END_REF]. How these optimization principles may be translated, integrated and combined into platform-wide practices largely remains an open and active question.

DATASET

We obtain song listening histories from Deezer, a French private music streaming platform which started operations in 2007. Deezer currently has about 14m monthly active users worldwide, about half of whom are paid subscribers as of January 2019. Our data set describes twelve months of anonymized activity over 2019 for 8,639 randomly chosen paying subscribers based in France who were registered to the service before December 31st, 2018 and active in January 2019. We limit ourselves to users with a paid subscription, even though a different listening behavior of users of the free service might be assumed from previous work [START_REF] Wlömert | On-demand streaming services and music industry revenues-Insights from Spotify's market entry[END_REF]. We discard events lasting less than 30s, assuming these are so-called "skips". The dataset ultimately totals about 51m timestamped streaming events (plays) describing which user listened to which song by which artist for how long i.e., 5.9k plays per user on average (or around 16 per day).

The data also indicates which product feature users accessed songs through. Note that the platform may be indifferently used from a dedicated desktop app, a mobile app, or directly from a browser: the interface generally provides the same functions irrespective of the chosen device. On Deezer, users may directly look for music titles, albums or artists using a search bar. They can tag songs, artists and albums as favorites and build their own playlists. We denote these modes of access as "organic" for they entirely rely on user choices, whereby users do look for a specific item in their or the platform's library. Users can also navigate to a home page where they find tailored recommendations which are either assembled and labeled by human editors at Deezer (such as recommended playlists variously called "10s electronic", "Rock & Chill", etc.) or algorithmically curated (such as the so-called "flow", which is a personalized automatic mix). We denote the former as "editorial", since the content is curated and recommended by human editors, and the latter as "algorithmic", for it entirely relies on an interaction between Deezer algorithms, platform-wide data and users' listening histories. In some cases, editorial playlists are algorithmically selected to be presented to users. We classify these as "editorial" since content selection remains primarily the choice of human editors. There is admittedly some porosity in the catalogs related to each of these three modes: for one, a user may include an algorithmically-or editiorially-discovered song into one of their playlists; similarly, algorithmic recommendation may feature songs a user already listened to organically. Transfers between various access modes have been analyzed in [START_REF] Shakespeare | Tracing Affordance and Item Adoption on Music Streaming Platforms[END_REF]. We focus on the properties of song listening portfolios associated to such and such type of user and affordance. Combining this analysis with transfers would make it possible to characterize adoption and influence dynamics in the mid-to long-term but remains beyond the scope of the present paper and is left for future research. Whenever a song is listened to through some access mode, we consider that it is because the user decided to rely on that access mode, and thus describes listening patterns associated to that mode, irrespective of their more distant origin.

We also collect comprehensive playlist histories for a selection of 39 mainstream radios in France over the same period. This includes the top 15 French national musical stations in terms of measured audience during 2019, along with a relatively arbitrary selection of more specialized stations and webradios. For each radio, broadcast logs were collected and songs matched against Deezer's whole catalog.

USER PRACTICES

Modes of access and user behavior classes

The quantitative literature does not often pay attention to the possible existence of distinct classes of users when it comes to their behaviors and listening habits on the platform, classes for which the function and effect of recommendation may differ significantly [START_REF] Garcia-Gathright | Understanding and Evaluating User Satisfaction with Music Discovery[END_REF]. Many studies report aggregate effects averaged over binary categories of users, for instance depending on a heavy vs. limited use of recommendation [START_REF] Datta | Changing their tune: How consumers' adoption of online streaming affects music consumption and discovery[END_REF][START_REF] Tien T Nguyen | Exploring the filter bubble: the effect of using recommender systems on content diversity[END_REF] or categorical variables such as gender [START_REF] Shakespeare | Exploring Artist Gender Bias in Music Recommendation[END_REF] or age [START_REF] Anderson | Algorithmic effects on the diversity of consumption on spotify[END_REF].

We assume (and confirm) that a pre-grouping of users depending on broad use classes may reveal distinct sensitivities to recommendation. In other words, we contend that users who, say, rely more on editorialized playlists may respond differently to algorithmic recommendation than users who are mainly organic.

Let us denote 𝑃 the number of plays in a user's listening history, of which proportions 𝑝 𝑎 , 𝑝 𝑒 and 𝑝 𝑜 = 1 -(𝑝 𝑎 + 𝑝 𝑒 )

have respectively been accessed algorithmically, editorially and organically. Their access mode profiles may thus be described by a triplet (𝑝 𝑎 , 𝑝 𝑒 , 𝑝 𝑜 ) defining barycentric coordinates in a ternary space, as shown in Figure 1-left. Even though a significant portion of users visibly rely to a large extent on the organic mode, we nonetheless observe a great deal of heterogeneity which hints at distinct use behaviors. We further define user groups by performing a simple Voronoi partitioning of profiles using a 𝑘-means algorithm. Choosing 𝑘 = 4 explains around 80% of the variance with limited improvement for 𝑘 > 4. Other clustering methods have been tried but generally yield a single cluster, most likely because data density increases roughly monotonously in the direction of the "organic" vertex, thereby preventing the formation of marked boundaries. As such, this partitioning only aims at defining bins as areas of the ternary space, rather than well-separated clusters per se. As a result, our four clusters should be understood as a simple approach to create an independent variable of use profiles among and between which we observe marked behavioral heterogeneity.

It is similar, albeit not equivalent, to defining, say, quartiles or deciles of income, which notoriously obey a hybrid log-normal/Pareto distribution with no clear-cut boundaries.

In the following we thus consider four user bins that we denote as "a" (rather "algorithmic", 989 users), "e" (rather "editorial", 655 users), "o" (rather "organic", 1614 users) and "o+" ("very organic", 5381). To avoid any ambiguity with the various other practical bins that we define and use later on, we will now denote these user bins as "user classes".

On the whole, organic classes (o and o+) comprise 7062 users i.e., roughly 80% of the dataset, for whom at least half of all plays have been accessed autonomously by users. Table 1 gives the shares of plays in each of the three modes for the centroids of these four classes. The number of plays 𝑃 is also a proxy of the user's activity on the platform. Its distribution spans several orders of magnitude, in a manner similar for all classes, as can be seen in Figure 1-rightin other words, there are weakly and strongly active users in all classes. We note that average activity is nonetheless slightly smaller for "editorial" users.

Two dimensions of diversity

We rely on these four classes to appraise the role of each access mode on music consumption, in terms of where each mode brings users to, and how much. We characterize the portfolio of songs the users listen to by focusing on two fundamental diversity measures:

(1) dispersion, denoting the lack of redundancy in the listening history;

(2) artist popularity, denoting the tilt toward songs by more popular artists.

We explain below (4.2.2) why we chose not to use genre meta-data to appraise diversity.

Dispersion and activity.

Dispersion may simply be computed as 𝑆/𝑃, where 𝑆 is the number of unique songs among the 𝑃 plays. It thus equals 1 when each song is played exactly once, and goes to 0 as plays of the same songs are repeated. In other words, low dispersion implies high redundancy of a listening history. 𝑆/𝑃 is also called "exploratory ratio" in [START_REF] Louail | Headphones on the wire Statistical patterns of music listening practices[END_REF] and further alludes to the trade-off between exploration and exploitation. Whichever the preferred interpretation, this ratio relates to a functional understanding of the diversity of a user's listening behavior. While the data display large fluctuations, we fit for each user class a linear model to highlight the general tendency. This reveals an inverse relationship between dispersion and activity, for all user types (see Figure 2-left): a user's catalog tends to saturate and its dispersion decreases with listening time (put differently, redundancy i.e., exploitation of the catalog increases). For a given activity level, dispersion is nevertheless lower for very organic users, while it is comparable for moderately organic and for recommendation-intensive users; i.e., as soon as some form of recommendation is involved.

This indicates a general inclination for redundancy with users who rely most on organic access modes. Focusing on recommendation-intensive users, dispersion is slightly lower for editorial users. However, their overall lower activity, which in turn corresponds to higher dispersion, leads to levels of dispersion comparable with those of algorithmic users, as shown on Figure 2-right.

We refine this picture by breaking down dispersion values per access mode. Figure 3 reveals that, for all user classes, the major access mode generally exhibits lower dispersion values -all the more so when activity is higher for a given access mode, as shown by the fact that the darkest bars (i.e., highest activity) are generally to the left of these histograms (i.e., lowest dispersion). Put simply, for algorithmic users (a), dispersion is lower for algorithmic recommendations and higher for editorial ones. For editorial users (e), dispersion is lower for editorial recommendations, and so on: the same applies to organic (o) and even more so for very organic users (o+) who exhibit high dispersion in both algorithmic and editorial access.

This suggests a phenomenon of specialization in each class of users, who tend to prioritize exploitation in their preferred mode of access, and favor exploration in the others, in terms of more dispersed plays. We shall here keep in mind that very organic users exhibit the lowest dispersion -using the platform heavily as a digital library connotes more exploitation of the catalog than using it as a digital librarian. In other words, even a moderate use of some form of recommendation is generally associated with a higher level of exploration.

Artist popularity and access modes.

Artist popularity, by contrast, describes music consumption in terms of content created by popular or less popular artists. We denote it as 𝜈. It relates to a semantic understanding of diversity. The literature traditionally proposes two main approaches to describe such diversity. On the one hand, some studies appraise diversity in spatial terms by hypothesizing an underlying "cultural" or music similarity space, and by embedding songs [START_REF] Airoldi | Follow the algorithm: An exploratory investigation of music on YouTube[END_REF][START_REF] Anderson | Algorithmic effects on the diversity of consumption on spotify[END_REF][START_REF] West | A model-based approach to constructing music similarity functions[END_REF], individuals [START_REF] Lambiotte | Uncovering collective listening habits and music genres in bipartite networks[END_REF][START_REF] Savage | Unravelling the omnivore: A field analysis of contemporary musical taste in the United Kingdom[END_REF] or both [START_REF] Hsieh | Collaborative metric learning[END_REF] into a graph or a low-dimensional space where proximity roughly corresponds to semantic similarity (e.g., similar musical genres or tastes). Such spaces are also used by platform algorithms to recommend songs not too far from one another (e.g., avoiding recommending manouche jazz after a heavy metal song).

On the other hand, some studies characterize consumption diversity through content popularity, most notably through the share of top artists [START_REF] Beuscart | Music recommendation algorithms and listener autonomy -The listening patterns of a panel of music streaming users[END_REF][START_REF] Datta | Changing their tune: How consumers' adoption of online streaming affects music consumption and discovery[END_REF]. We follow here this latter approach for three main reasons.

First, designing an embedding space requires choosing between many possible similarity metrics and construction approaches, each based on strong hypotheses on the semantic encoding. For instance, distances based on the cooccurrences of content tags (e.g. taxonomies [START_REF] Hennequin | Audio based disambiguation of music genre tags[END_REF] or folksonomies [START_REF] Park | Understanding musical diversity via online social media[END_REF]), will typically suffer from definition ambiguities and socio-cultural inconsistencies [START_REF] Beer | Genre, boundary drawing and the classificatory imagination[END_REF][START_REF] Elena V Epure | Modeling the Music Genre Perception across Language-Bound Cultures[END_REF] and more prosaically from annotation noise and biases. Distances based on acoustic similarities [START_REF] Van Den Oord | Deep content-based music recommendation[END_REF] or usage [START_REF] Hsieh | Collaborative metric learning[END_REF] are typically tailored for neighborhood consistency, but will not generally bear any meaning for, say, the distance between metal and jazz songs, compared with the distance between jazz and classical pieces. In addition, many users, particularly omnivores [START_REF] Richard | Changing highbrow taste: From snob to omnivore[END_REF][START_REF] Van Eijck | Social differentiation in musical taste patterns[END_REF] may show interest for more than one genre. Navigation profiles may thus exhibit several distinct centroids in possibly distant regions. In turn, this potential "musical polycentrism" might blur the meaning of notions solely based on the geometric extent of listening profiles in multi-dimensional spaces. Conversely, artist popularity remains a mono-dimensional notion, whose mean and deviation are simple yet likely robust indicators of the position and span of a user's musical content consumption with respect to the whole field.

Second, this will ease the comparison with radio playlists and thus offline editorial recommendation. The radios of our dataset indeed address a quite diverse collection of music genres, some being very generalist (e.g., 'FIP'), some much more specialized (e.g., 'TSF Jazz'). To discuss specialization and eclectism across genres and radios, we believe that artist popularity may act as a better sort of lingua franca than, say, extents in a vector space loosely encoding cultural similarities.

Third, artist popularity directly connects with an older debate on whether the almost infinite catalogs of online platforms foster consumption of more mainstream or more niche content, or both, and by which types of users [START_REF] Elberse | Should you invest in the long tail?[END_REF].

We first define artist popularity by computing how many times their songs have been played in the whole dataset as a proxy of their popularity on the platform. This is referred as "artist playcounts" in [START_REF] Bauer | Global and country-specific mainstreaminess measures: Definitions, analysis, and usage for improving personalized music recommendation systems[END_REF], also connected with the mainstreamness of artists. We then distinguish four bins of popularity such that each bin gathers a similar numbers of plays i.e., artists which, taken together, represent the same total amount of plays ( 1 4 users 𝑃). This ensures that a play chosen in a uniformly random way from the listening history has the same likelihood of belonging to any of the four bins. As a result, the first bin 𝜈 1 gathers the top 73 artists, the fourth bin 𝜈 4 the bottom 166,869 artists. Table 2 gathers the proportion of access modes for each popularity bin. In general, songs are principally listened to organically, irrespective of artist popularity -around 80% of all plays on average, which is assuredly expected given the prevalence of organic access modes (figure 1). We however see that organic access is non-monotonous, in that the bin # artists access mode Finally, we observe that dispersion and artist popularity are associated. Part of it is likely mechanical: since the most popular bin features much less artists as well as less songs (18,425 songs for 𝜈 1 vs. 1,161,257 songs for 𝜈 4 ), it also induces a lower likelihood of dispersion, all other things being equal. Notwithstanding, we essentially observe that users who consume content by less popular artists exhibit more dispersed listening histories; see Figure 4-left. We refine this picture by computing the dispersion of the listening history of each user restricted to songs of a given popularity bin, shown in the right panel of Figure 4, which also decreases for content made by popular artists.

To summarize, average dispersion increases with activity and decreases with artist popularity. Since very organic users have a lower dispersion, this further hints at a positive relationship between the use of recommendation and dispersion.

User types and access mode biases

We may now appraise the interplay between user types, access modes and diversity from the user perspective. Let us start with artist popularity. For each user, we compute the proportion of plays that fall in each popularity bin and divide it by its expected value i.e., we use a null hypothesis where all plays would uniformly fall in equal amounts into each bin (typically proportional to 𝑃/4 by construction of popularity bins). These ratios yield a divergence profile for each user in terms of their appetency for some bins over others. We then average these profiles over all users of each class and plot in Figure 5 (top panel) the mean over-or under-consumption per popularity bin.

We find that algorithmic users (a) rather under-consume content by popular artists while editorial users (e) exhibit an almost opposite profile by over-consuming such content. Interestingly, o and o+ users markedly differ in their appetency for popular artist content: whereas very organic users tend to slightly over-listen to songs from both the most and the least popular artists [again, consistent with consumer behavior on retail platforms 18], organic users exhibit a monotonous profile favoring less popular content in a strictly increasing manner; in this regard, they resemble more algorithmic users.

We refine this analysis by further plotting over-and under-consumption with respect to access modes. More precisely, given a user type, we perform the normalization locally for each access mode: the ratio between actual and expected

ν 1 ν 2 ν 3 ν 4 ν 1 ν 2 ν 3 ν 4 ν 1 ν 2 ν 3 ν 4 ν 1 ν 2 ν 3 ν 4 -0.4 -0.2 0
ν 1 ν 2 ν 3 ν 4 ν 1 ν 2 ν 3 ν 4 ν 1 ν 2 ν 3 ν 4 ν 1 ν 2 ν 3 ν 4 -4 -2 0
Fig. 5. Relative consumption of content from each popularity bin, average log-ratio with respect to a uniformly random baseline for each bin (0 corresponds to no deviation, the x-axis is ordered from 𝜈 1 to 𝜈 4 i.e., for musical content from more to less popular artists).

Top: average over all plays. Bottom: breakdown by access mode.

quantities is computed using respectively 𝑝 𝑎 𝑃, 𝑝 𝑒 𝑃 and 𝑝 𝑜 𝑃 instead of 𝑃. The results are shown on the lower panel of figure 5. For instance, the curve that corresponds to, say, editorial access of o+ users, indicates to what extent their editorial plays fall into each popularity bins.

We generally confirm that algorithmic access tends to correspond to content from less popular artists, even for very organic users (o+) who normally over-consume content from popular artists, and also for editorial users (e) who normally consume even more content from popular artists, yet to a lesser extent. By contrast, on the whole, and for all user types, editorial access pulls towards popular artists. Organic access, finally, tends to somewhat mimic average behavior (and expectedly all the more so for the most organic users), but in a less marked manner, suggesting that a good part of the deviation in trends observed on average values stems from recommendation-based access modes, be it editorial or algorithmic.

More broadly, these observations contribute to shed light on a typical chicken-and-egg problem i.e., whether access modes (and thus platform features and affordances) influence user behavior, or user behavior influences how access modes are being used, and for what. In effect, if we focus on organic access as a reference of what users autonomously look for on the platform, we see that user classes exhibit markedly different appetencies, for instance with respect to content from least popular artists. We also know that user classes roughly entail specialized ways of using the platform, whereby dispersion is lower for the main corresponding access mode (as per Figure 3), which indicates that the major access mode leans more toward exploitation than exploration. Further, the use of recommendation, algorithmic or not, appears to tilt consumption towards more exploration, all other things being equal. This is further emphasized by the fact that editorial users exhibit a higher dispersion on average than very organic users, even if they generally consume more popular content which is otherwise related to lower dispersion in aggregate. If we now shift to the use of recommendation-based access modes, we see that they tend to exhibit a general pattern, irrespective of user types: editorial favors popular, algorithmic leans toward least popular, in very broad and rough terms. In this regard, Figure 5 contributes to disentangle how both types of effects yield a general consumption profile -i.e. both due to user types and access modes. It is legitimate to suggest here that we observe and, at least in part, deconstruct the intertwinement of both (1) underlying user types, corresponding to different ways of using the platform, and (2) overlaying access modes, corresponding to the different ways in which the platform may affect user consumption.

THE DIVERSITY OF HUMAN-ASSISTED GUIDANCE

Notwithstanding the preferences and expectations of users on the platform, the picture that emerges is that of a split between two types of recommendation in terms of fostering diversity: irrespective of dispersion trends, editors rather than algorithms appear to sustain the consumption of songs from popular artists (and vice versa for least popular artists). To put this observation in perspective, we need to rely on an external reference. We contend that radio programs constitute a relevant instance in this regard. Radio-based playlists can be construed as one of the closest offline equivalent of editorial playlists on Deezer -and, from a human computing viewpoint, one of the oldest large-scale music recommendation systems.

In practice, it would be difficult to access detailed radio listening histories for a number of people, let alone for the subset of users we considered here. To circumvent this issue, we adjust the way we carry out computations on users to make both sources as comparable as possible. On the one hand, we use artist popularity values from the Deezer data set as a general proxy. Around 83% of songs played on radios are matched with the user data set. These songs inherit their respective artists' popularity computed from the Deezer data, and we ignore unmatched songs. By construction, this likely induces an overestimation of popular content, and, in turn, of the popularity bin for radios that play less popular artists.

On the other hand, we define hourly listening sessions for both users and radios. This additional focus on hours aims at taking into account the fact that radio playlist may be heavily shaped by the existence of programs broadcast at specific moments of the day, or night. Concretely, for each radio and each user we consider their time-ordered sequence of plays over the year, and we setup counters to keep track of the number of plays and hour ℎ + 1 during the entire period, along with the number of new songs 𝑆 (ℎ) that were played during this hour, that is, songs that had never been played previously by this radio (resp. by this user). This way for each radio and user we calculate twenty-four hourly 𝑃, 𝑆, 𝑆/𝑃 and ν values. We then averaged these hourly values over users that belong to the same class, and compare the four user classes previously identified with radio stations, according to the range of their hourly dispersion 𝑆/𝑃 and hourly average popularity ν values.

Results are gathered on figure 6. We select a representative sample of 15 radios out of 39 for clarity purposes. On the left panel, we compute dispersion boxplots both for radios and user types. All items, radios or user types, are ordered from top to bottom by decreasing value of average dispersion. We further color boxplots according to the average popularity bin. Table 3 additionally gathers the detailed breakdown of plays in each popularity bin, for all user types and a few selected broadcasters.

We observe that most user types exhibit more dispersion than most radios, indicating that radio programming is tilted toward the exploitation of a more limited catalog. More precisely, there appears to be an inflection point around "TSF Jazz" and "RFM" which roughly splits the set of items between a larger half with a significantly low dispersion (below 0.10) and a smaller half with much higher dispersions (generally above 0.25). In this picture, user classes exhibit among the highest values. Remarkably, two radios are above all user classes -France Musique and FIP, which are public-funded, predominantly musical and rather eclectic broadcasters. Besides, a mild correlation between popularity and dispersion is visible: the diversity of the catalog in terms of distinct played items is roughly linked to its diversity in terms of playing artists from the less popular bins.

A dual computation consists in representing boxplots of observed mainstreamness averaged over hours, while coloring them with the average dispersion -see the right panel of Figure 6. While the correlation between dispersion and popularity is not immediately visible, the Spearman rank correlation between S/P and the proportion of songs in 𝜈 4 is equal to 0.827, confirming the similar inverse ordering of dispersion and popularity: radios with more dispersed programs also play more songs from less popular artists. There are notable exceptions such as "Radio Meuh", whose lower bound on popularity is the highest of all radios -and it is indeed considered informally as a very eclectic broadcaster-while having a relatively moderate dispersion (as seen in Table 3). The new interesting take-away of this second plot lies in the positions of user types. They are now much closer to the median value of this selection, even though organic and algorithmic users appear to be a little bit above it. Put differently, while online music listening practices seem to foster functional diversity (dispersion), in terms of semantic diversity (popularity) they seem, on average, to be neither significantly above nor significantly below the mass of the radios we focus on.

CONCLUDING REMARKS

Our analysis of recommendation, in the broad sense, on a music streaming platform started by assuming the existence of distinct attitudes towards platform affordances. This produced a typology of four user classes who markedly differ in their modes of access to music and, more importantly, in the way these modes are associated with distinct effects on the diversity of consumed songs. We showed more broadly that there is no blanket answer to the question of the influence of recommendation devices: rather, we contend that it primarily depends on users. This observation may have important ramifications in the appraisal of the effect of recommender systems on consumption diversity -we suggest to speak of filter niches, rather than bubbles.

Moreover, we showed that the framing of recommendation on platforms and, thus, their algorithmic governance, would benefit from paying specific attention to the various types of guidance. Human-mediated curation is associated with distinct effects on the exploration of content and fostering diversity, and with distinct user classes. Both types of guidance seem to often have opposite effects. They may also fulfill distinct roles and thus have to obey to distinct design principles. We further introduced a bridge between platform-based recommendation and traditional offline curation, exemplified by radio playlists, which we see as a fruitful point of comparison to frame how platforms may or may not affect user preferences and access to content. If user classes were radios (and assuming it is valid to speak of an average user for each user class), they would certainly not appear to be more repetitive than most radio stations, while they would exhibit a wide range of serendipity. Interestingly, while algorithmic access modes seem to generally be associated with an avoidance of popular content, it is what we call organic users who appear to focus most on the least popular content -yet, these users precisely exhibit a relatively balanced diet of platform affordances, generally combining their autonomous navigation with both sorts of recommendation. In other words, we may hypothesize that the most "expert" users best exploit the platform capabilities to explore the long tail. Editorial access, on the other hand, and even more so for editorial users, appears to fulfill a role traditionally ascribed to mainstream radios -putting forward a higher proportion of popular artists.

A step further from this study would consist in analyzing temporal aspects of the partitioning. Indeed, the chronology of access modes to a song probably carries valuable information. For instance, a song may first be discovered through an editorial recommendation, then later accessed organically and symmetrically, organically accessed content may be subsequently picked by the algorithm later on. More generally, user trajectories and transitions between classes should be the focus of future research that would shed light on the acclimation of users to platform features. In particular, the causal relationship that may exist between the presence or absence of some content in editorial and algorithmic recommendations and the evolution of their platform-wide popularity would also be a fruitful field of investigation.

With respect to the ubiquitous debate on whether platform recommendation fosters diversity or not, a mixed picture emerges depending on which types of recommendation one is talking about, as well as which type of audiencewhereby radios provide an insightful reference. On the whole, this comparison may shed light on the relative position of platforms and their contribution to cultural diversity with respect to traditional cultural prescribers and, again, how their algorithmic principles should be governed. Understanding user expectations not only in terms of genres and tastes, but in terms of their use and perhaps understanding of the technical features of a platform, may help refine the design of recommender systems ex ante, rather than optimizing their results ex post. The corresponding takeaway for practitioners is to be attentive to the differences between access modes which may fulfill distinct roles for listeners e.g., active exploration vs. background music listening. Longitudinal analyses of the evolution of user tastes, specifically in terms of learning and of long-term effects of distinct platform affordances, as well as qual-quant analyses based on user surveys and interviews would be most helpful in further disentangling the chicken from the egg.

Fig. 1 .

 1 Fig. 1. Left: Use profiles and classes, where each dot on the ternary plot corresponds to a user of barycentric coordinates (𝑝 𝑎 , 𝑝 𝑒 , 𝑝 𝑜 ), and each color refers to one of the four classes a (blue), e (red), o (green), o+ (yellow). Right: Box and violin plots of activity (number of plays 𝑃 , log-scale) for each user class.

Fig. 2 .

 2 Fig. 2. Dispersion profiles for each user class. Left: scatterplot (each dot is a user) and binned averages (solid lines) as a function of activity (𝑃 , log-scaled). Right: boxplots per user class.

Fig. 3 .

 3 Fig. 3. Breakdown of dispersion values for each user class and for each access mode. Histograms are further binned by deciles of increasing 𝑆/𝑃 values (from 0 to 1 from left to right) and indicate how many users of each class (a, e, o and o+) exhibit which dispersion value for a certain access mode (algorithmic, editorial or organic). Average activity values for users of each decile bar are further indicated by a grayscale, where darkest shades correspond to highest 𝑃 values.

Fig. 4 .

 4 Fig. 4. Artist popularity and dispersion. Left: dispersion of listening histories as a function of the average artist popularity profile of each user ν. Each dot is a user, the solid line represents the best linear fit as a guide to the underlying trend. Right: boxplot of dispersions restricted to content of a certain popularity bin.

Table 1 .

 1 Population of each user class and proportion of plays by access mode for users chosen as class centroids (rows sum to 100%).

	user	population		access mode share
	class #users (% dataset)	organic algorithmic editorial
	a	989 (11%)	36%	58%	6%
	e	655 ( 8%)	55%	7%	38%
	o	1614 (19%)	70%	23%	7%
	o+	5381 (62%)	94%	2%	4%

Table 2 .

 2 Proportion of access modes for each artist popularity bin (preferred bins for each access mode are marked in bold).highest shares are found in both the most and least popular artist bins [consistentwith 18]. A different picture emerges for guided access modes. Algorithmic access puts the highest share on intermediate bins, and by far the lowest share on the highest popularity bin. Editorial access, by contrast, is monotonously more frequent for higher popularity bins. In other words, content by popular artists seems to be more often proposed by editorial rather than algorithmic picks. To further exhibit this effect, we compute the average popularity bin for each access mode and find 2.68 for algorithmic plays, 2.49 for organic ones, and 2.23 for editorial ones (the average popularity bin for all plays is 2.50, by construction).

			algorithmic editorial organic
	𝜈 1	73	9%	8%	83%	100%
	𝜈 2	319	16%	8%	76%	100%
	𝜈 3	1462	18%	5%	77%	100%
	𝜈 4	166869	15%	5%	80%	100%
	all	164955	14%	7%	79%	100%

  𝑃 (ℎ) that occurred between hour ℎ Fig. 6. Dispersion and artist popularity for a selection of radios and the four user classes. Boxplots are computed on hourly values. Left: dispersion ranked by decreasing average values, colored by average popularity bins. Right: dually, popularity ranked by decreasing average bin number, colored by average dispersion.

	Chante France RTL2 NRJ Skyrock Fun Radio Générations Mouv' Latina RFM TSF Jazz Radio Nova Radio Meuh o+ Radio Classique o a e Fip France Musique			ν	2.0 2.5 3.0 3.5	Skyrock NRJ Mouv' Générations e RFM o+ Chante France RTL2 a France Musique Radio Meuh Radio Nova TSF Jazz Fip Radio Classique Fun Radio Latina o		S/P	0.2 0.4 0.6
	0.00	0.25	0.50 S/P	0.75		2	ν	3	4

Table 3 .

 3 Average breakdown of content played into each popularity bin, for all user types and a selection of radios, and average dispersion.

		𝜈 1	𝜈 2	𝜈 3	𝜈 4	⟨𝑆/𝑃 ⟩
	a 17% 27% 29% 27%	0.39
	e 29% 30%	22% 19%	0.41
	o 22% 25% 26% 27%	0.38
	o+ 29% 23% 23% 25%	0.28
	Radio Meuh	0%	2% 16% 82%	0.23
	FIP	2%	7% 20% 71%	0.60
	RFM	7% 27% 36% 30%	0.10
	Fun Radio 18% 61% 13 %	8%	0.04
	NRJ 41% 23% 23%	7%	0.03

ACKNOWLEDGMENTS

This paper has been partially realized in the framework of the "RECORDS" grant (ANR-2019-CE38-0013) funded by the ANR (French National Agency of Research). We are grateful to Dougal Shakespeare for useful comments.


J Lacaze Cirimat

I Asenjo

S Méndez

J Sertucha

P Larrañaga

R Suárez

Ljxuh 3krwrjudsk Ri

Wkh Zkroh

D [ Ldo

Vhfwlrq Ri

D Fxelf

Eorfn Fp

L Q Vl]h 7kh

Zklwh Duurzv

Vkrz Wkh

Olplw Ehwzhhq

Wkh Rxwhu

Rqh Dqg

Wkh Lqqhu

Zlwk &+

',),&$7,21 $662&,$7(' 72 &+81.< *5$3+,7( ,1 +($9<6(&7,21 '8&7,/( ,521 &$67,1*6

$EVWUDFW

Heavy-section castings made of spheroidal graphite cast irons are known to be prone to graphite degeneracy. Upon the various degenerate forms of graphite reported in the literature, chunky graphite is the most common and detrimental one. A great deal of effort has been made for many years to prevent its formation but no convincing description of the factors controlling its appearance has been given so far.

In large-size castings, chunky graphite generally appears away from the surface and its occurrence is made evident on a metallographic section by a darker contrast. Because of this sharp and clear transition between the non-affected and the affected zones, several authors looked for chemical heterogeneities at the scale of the part but all concluded to the absence of macrosegregation. This paper presents experimental evidence based on differential thermal analyses that metallurgical differences do exist in samples machined out of the affected and nonaffected zones of a single cast block.

Keywords: cast iron, heavy section, graphite degeneracy, chunky graphite

,QWURGXFWLRQ Heavy-section castings made of spheroidal graphite cast irons are known to be prone to graphite degeneracy. [START_REF] Elliott | Cast Iron Technology[END_REF] Upon the various degenerate forms of graphite reported in the literature, chunky graphite (hereafter denoted as CHG) is the most common and detrimental. A great deal of effort has been made to prevent its formation and it has been found that use of chills as well as minute additions of Sb are amongst the most efficient. [START_REF] Javaid | Production of Heavy-Section Ductile Cast Iron[END_REF] Both actions have however their own drawbacks, chills being limited to sections a few centimetres thick while the addition of Sb (and other "counter-active" elements) is complicated because the necessary amount lies in a window that depends on the casting section and on other trace elements present and because Sb is a pearlite promoter.

CHG is a degenerate form of graphite that is mainly observed in the thermal centre of large spheroidal graphite (SG) castings, [START_REF] Karsay | Control of Graphite Structure in Heavy Ductile Iron Castings[END_REF][START_REF] Strizik | Contribution to the Mechanism of Formation of Chunky Graphite[END_REF][START_REF] Liu | SEM Study of Chunky Graphite in Heavy Section Ductile Iron[END_REF] but may also appear in thin sections of ductile iron castings containing high Ce and Si contents, [START_REF] Asenjo | Microstructure Investigation of Small-Section Nodular Iron Castings with Chunky Graphite[END_REF] besides austenitic Ni-alloyed cast irons. [START_REF] Gagné | Effects of Wall Thickness on the Graphite Morphology and Properties of D5-S Austenitic Ductile Iron[END_REF] In large-size castings, CHG appears away from the surface and its formation becomes clear on metallographic sections by a darker contrast as illustrated in Figure 1. Numerous attempts have been made to describe the metallurgical process leading to the formation of CHG, but no convincing theory has been established until now.

Because of the sharp and clear transition seen in Figure 1 between the non-affected and the affected zones, several authors looked for chemical heterogeneities but all concluded to the absence of macrosegregation. [START_REF] Gagné | Heavy Section Ductile Iron Castings -Part I: Structure and Properties[END_REF][START_REF] Källbom | Chunky Graphite in Ductile Iron Castings[END_REF][START_REF] Prinz | Investigation of Causes of Graphite Degenerations of SG Iron like Chunky Graphite[END_REF][START_REF] Mendez | Improved Analytical Method for Chemical Analysis of Cast Irons Application to Castings with Chunky Graphite[END_REF] It should be recognized however that the analysis methods used are obscured by detection limits and accuracies that are not always clearly stated. Moreover, they all estimate global compositions and are not able to differentiate if a particular species exists in an atomic state or bound within a compound. This paper presents differential thermal analysis (DTA) experiments performed on samples machined from affected and non-affected zones of a single cast block. The DTA records show that there are in fact metallurgical differences between these two zones.

• heating to 1200C (2192F), holding 1 sec. then cooling at 5, 10 or 15ºK/min (in this latter case, the upper temperature of the heating stage was increased to 1225C (2237F) in order to ensure complete melting of the sample before cooling starts).

In the first series of trials, the lengthy holding in the liquid state was designed so as to lead to full Mg fading and solidification with lamellar graphite. On the contrary, the trials with very rapid melting and short stay in the liquid state were expected to preserve alloy composition as much as possible. One additional trial consisted in applying a rapid melting and solidification at 10ºK/min down to 1000C (1832F), then reheating at 1200C (2192F) and holding 1800 sec., finally solidifying at 10º K/min. This trial was defined for reproducibility checking.

Independent calibration of the DTA cell with pure aluminium and nickel showed that it underestimated temperatures by about 3C. All records presented in the following have been corrected accordingly.

5HVXOWV

The graphs in Figure 3 show the whole series of DTA records obtained upon cooling after sufficient time has been spent in the liquid state so that all the Mg introduced for spheroidization has faded. In these graphs, the vertical dashed line indicates the calculated temperature for the stable eutectic. It is seen that the records show one main peak associated to the eutectic reaction, and a much smaller thermal arrest at higher temperatures. Comparison of the peaks associated to the eutectic reaction in Figures 3-a for with-CHG and 3-b for no-CHG materials shows that the DTA records on both materials are similar whatever the cooling rate, from 2.5 to 20ºK/min. As a matter of fact, the change in the cooling rate

)LJXUH 2SWLFDO PLFURJUDSKV RI WKH FDVW PDWHULDO WDNHQ D LQ WKH QRQDIIHFWHG RXWHU DUHD DQG E LQ WKH FHQWUDO SDUW RI WKH EORFN D E ([SHULPHQWDO ,QYHVWLJDWLRQ ([SHULPHQWDO 'HWDLOV

A cubic block 30 cm in size was cast following a procedure detailed previously. [START_REF] Asenjo | Effect of Mould Inoculation on the Formation of Chunky Graphite in Heavy-Section Spheroidal Graphite Cast Iron Parts[END_REF] The composition of the material as analyzed after casting was 3.68% C, 2.20% Si, 0.09% Mn, 0.035% P, 0.014% S, 0.040% Mg, 0.02% Cu, 0.005% Ti, 0.02% Cr, 0.011% V, 0.0123% Ce, 0.002% La (contents expressed in weight). Subsequent analyses made on an area with CHG graphite and another free of this defect did not show any chemical differences. According to a previous evaluation of the effect of various elements on the austenite and graphite liquidus, [START_REF] Castro | Simulation of Thermal Analysis Applied to the Description of the Solidification of Hypereutectic SG Cast Irons[END_REF] this alloy is slightly hypoeutectic (carbon equivalent at 4.30%), the austenite liquidus temperature is 1167.6C (2133.7F) and the equilibrium eutectic temperature is 1158.3C (2116.9F). The micrographs in Figure 2 present the microstructure in the outer non-affected area (Figure 2-a) and in the inner zone (Figure 2-b). In this latter, several CHG cells are clearly visible. The central area affected with CHG (see Figure 1) amounts to 17.6% of the whole volume of the block, while the specific surface of CHG cells is as high as A A = 25.0% in the central part.

Samples for DTA were machined in the outer area free of CHG (labelled no-CHG in the following) and from the centre (labelled with-CHG). The study specimens were cylinders 3.9 mm in diameter and 4 to 5 mm in length.

The DTA experiments were designed to look for any differences in the cooling records that could be related to the origin of the samples, either with-CHG or no-CHG. Two series of trials were performed with one new sample for each run:

• heating to 1200C (2192F), holding 1800 sec. then cooling at either 2.5, 5, 10 or 20ºK/min;

)LJXUH (IIHFW RI FRROLQJ UDWH RQ VROLGL¿FDWLRQ RI D ZLWK&+* DQG E QR&+* PDWHULDOV DIWHU KROGLQJ DW & WR HOLPLQDWH 0J 7KH YHUWLFDO GDVKHG OLQH UHSUHVHQWV WKH FDOFXODWHG HXWHFWLF WHPSHUDWXUH D E

effects similarly undercooling for the onset of the eutectic reaction and the shape of the eutectic arrest of both the with-CHG and no-CHG materials.

The micrographs in Figure 4 show the microstructure of both materials after cooling at 10ºK/min. where it is observed that solidification led effectively to the same microstructure consisting in a lamellar graphite eutectic at the outer surface of the samples which then transforms to undercooled graphite in the central areas. The presence of a significant amount of austenite dendrites allows the peak above the eutectic temperature to be related to primary deposition of austenite, in agreement with the hypoeutectic nature of the alloy. It may be noted in Figure 3 that the start temperature for this peak varies from one sample to another in an "apparently" erratic way, namely apparently without any relationship with the cooling rate or with the material (i.e. with-CHG or no-CHG). A possible explanation could be that the sampling procedure for machining DTA samples induced slight change in the actual carbon content from one sample to another. Such a difference would lead to a change in the observed liquidus temperature without affecting the eutectic reaction itself. Such a sensitivity to sampling may simply be related to the fact that the characteristic size of the microstructure in the blocks, either austenite dendrites or CHG cells, is of the same order as the size of the blanks used for DTA.

A further comparison of the microstructure obtained after a DTA run is given in Figure 5 for samples solidified at 2.5ºK/ min. It is seen that lamellar graphite shows the same features for both with-CHG and no-CHG materials mainly consisting of coarse graphite lamellae. This change in the graphite morphology with respect to Figure 4 is a consequence of the reduction in the cooling rate and thus in the graphite growth rate from liquid.

In Figure 6 we compare the DTA traces recorded during the first and second coolings of the additional trial carried out for the no-CHG material. The vertical interrupted line represents, as before, the calculated stable eutectic temperature. The main differences between these two records show up during the eutectic reaction, which consists of two and one peaks for the first and second cooling records respectively. The same behaviour was observed for the with-CHG material. It is noteworthy that the first eutectic peak during the first cooling starts at nearly the same temperature as the single eutectic peak during the second cooling. This suggests relating it to an initial eutectic solidification with lamellar graphite also for the first cooling. However, after this short initial transformation, the main eutectic reaction during the first cooling takes place at a much higher undercooling that is more typical of compacted-vermicular (CVG) or spheroidal (SG) graphite.

The graphs in Figure 7 compare the DTA curves recorded for various cooling rates on with-CHG (solid lines) and no-CHG (dotted lines) materials after a very short stay in the liquid state. In these graphs, the reference line corresponding to the stable eutectic temperature has been superimposed as shown in Figure 3. The corresponding microstructures are illustrated in Figure 8. Looking first at the records obtained with no-CHG samples (dotted lines in Figure 7), it is seen that they all show the same features for the eutectic reaction, i.e. a small peak starting at about the stable eutectic temperature and a main peak at significant undercooling. The microscopic observations showed effectively very little lamellar graphite as illustrated in Figure 8 (column to the right) and the bulk material has solidified with a mix of vermicular and spheroidal graphite.

)LJXUH 0LFURJUDSKV RI ZLWK&+* D DQG F DQG QR&+* E DQG G '7$ VDPSOHV DIWHU PHOWLQJ DW & KROGLQJ IRU V DQG FRROLQJ DW .PLQ 0LFURJUDSKV F DQG G ZHUH WDNHQ DW WKH OLPLW EHWZHHQ WKH RXWHU ODPHOODU ]RQH DQG WKH LQQHU XQGHUFRROHG DUHD D E F G )LJXUH 0LFURJUDSKV RI D WKH ZLWK&+* DQG E QR&+* '7$ VDPSOHV DIWHU FRROLQJ DW .PLQ D E

In contrast with the DTA records obtained from the no-CHG material, those obtained for with-CHG show features apparently varying with the cooling rate. Considering firstly the records for the slower and higher cooling rates for the with-CHG material, it is seen they appear similar to those for the no-CHG material, though extended over a slightly larger temperature range. Comparing the corresponding microstructures illustrated in Figure 8 (column to the left), it is noted that the with-CHG samples present a higher number of nodules than no-CHG samples. For the intermediate cooling rate of 10ºK/min, the DTA record on the with-CHG material also shows two peaks during the eutectic reaction, but in this case of similar amplitude (in contrast with all other records). Looking at the corresponding micrograph in Figure 8 (note that the scale is not the same as for the other samples), it is seen that these two peaks may be easily associated with a two-step solidification of the sample, the outer shell with lamellar (undercooled) eutectic and the inner part with nodular/vermicular eutectic. As for the other cooling rates, it should be stressed that the nodule count in the central area is much higher for the with-CHG material than for no-CHG.

The reproducibility of the DTA traces recorded at a cooling rate of 10ºK/min was checked with the additional trial mentioned previously. For both the with-CHG and no-CHG materials, it was found that the record for the first cooling was similar to that after rapid melting and immediate cooling, while the second record after holding was similar to the one of the first series of DTA runs which includes a high temperature holding. This underlines the peculiarity related to the 10ºK/min cooling rate, namely that the difference of the DTA records for with-CHG and no-CHG materials at that particular cooling rate, is reproducible.

)LJXUH &RPSDULVRQ RI WKH '7$ WUDFHV UHFRUGHG GXULQJ WKH ¿UVW DQG VHFRQG FRROLQJV RI WKH DGGLWLRQDO WULDO LQ WKH FDVH RI WKH QR&+* PDWHULDO 7KH YHUWLFDO GDVKHG OLQH UHSUHVHQWV WKH FDOFXODWHG WHPSHUDWXUH RI WKH VWDEOH HXWHFWLF )LJXUH &RPSDULVRQ RI WKH '7$ UHFRUGV REWDLQHG XSRQ FRROLQJ RI ZLWK&+* VROLG OLQHV DQG QR&+* GRWWHG OLQHV PDWHULDOV DIWHU YHU\ VKRUW KROGLQJ LQ WKH OLTXLG VWDWH &RROLQJ UDWHV ZHUH D .PLQ E .PLQ DQG F .PLQ 7KH YHUWLFDO GDVKHG OLQH UHSUHVHQWV WKH FDOFXODWHG

'LVFXVVLRQ

The higher nodule count observed in re-solidified material from the with-CHG areas as compared to no-CHG samples is considered to be due to metallurgical differences between the materials. As no significant chemical heterogeneities are expected, [START_REF] Gagné | Heavy Section Ductile Iron Castings -Part I: Structure and Properties[END_REF][START_REF] Källbom | Chunky Graphite in Ductile Iron Castings[END_REF][START_REF] Prinz | Investigation of Causes of Graphite Degenerations of SG Iron like Chunky Graphite[END_REF][START_REF] Mendez | Improved Analytical Method for Chemical Analysis of Cast Irons Application to Castings with Chunky Graphite[END_REF] this suggests that elements such as magnesium that favour spheroidal growth got bound as compounds in the with-CHG area when the block solidified. This could be in line with the observation of Källbom et al. [START_REF] Källbom | Chunky Graphite in Ductile Iron Castings[END_REF] who noticed the presence of numerous inclusions in the heavy section castings they studied, that contain Mg and S but not O in the chunky cells, while in areas with spheroidal graphite and at the with-CHG cell borders particles containing Mg, O and Si were observed. The fact that the solidification behaviour of with-CHG and no-CHG materials is identical after the melt has been held for some time at 1200C (2192F) suggests that the precipitates considered above appear below 1200C (2192F) during the slow cooling of heavy section castings. A tentative schematic of metallurgical evolution during DTA experiments could be that remelting the material led to immediate volatilization of magnesium in the case of no-CHG material, while this step was preceded by the dissolution of the compounds in the case of with-CHG material. This extra time gave rise to a higher level of magnesium available during re-solidification of with-CHG samples than of the no-CHG ones, thus explaining that more spheroidal graphite was observed in the former. The sensitivity of the DTA records to the cooling rate in the case of the with-CHG material should thus be related to time-dependent dissolution/precipitation processes of compounds in the liquid cast iron.

&RQFOXVLRQ

After holding the with-CHG and no-CHG materials in the liquid state long enough for them to be freed of any nodularizing element, their solidification proceeds similarly by deposition of a coupled eutectic with lamellar or undercooled graphite. The eutectic reaction starts with similar and low undercooling with respect to the stable eutectic temperature, and no significant change in the rate of growth could be detected from the DTA curves which could be related to the change from lamellar to undercooled graphite.

When the material is kept for a very short period in the liquid state before cooling, solidification starts again with lamellar graphite but then this reaction slows down until a high enough undercooling is reached when spheroidal and vermicular graphite may grow. Re-solidification of with-CHG material gives rise to a higher nodule count than no-CHG material, and this suggests that nodularizing elements become bound in compounds during the lengthy eutectic solidification period of heavy-section cast blocks. While this does not give rise to any overall chemical heterogeneity when comparing with-CHG and no-CHG areas, the process does affect the amount of nodularizing elements actually available in the remaining liquid. The exact process and the nature of the compounds involved are still to be investigated.

Authors:

We do agree that other elements may play a role, as noted in the beginning of the discussion section.

The emphasis was put on magnesium because it is by far the main spheroidizing element in the investigated alloy.

Reviewer:

The authors only reference one thermal analysis paper; many have been previously published that appear to explain the data quite nicely. Secondly, phase transformation temperatures are known to be a function of cooling rate.

Authors: The paper dealing with thermal analysis was referenced only because it contains the information for calculating the stable eutectic temperature. The effect of cooling rate on the characteristics of cooling curves obtained by thermal analysis or differential thermal analysis is effectively so well known that it did not appear necessary to elaborate on that. The curves were shown for comparison purpose, namely discussing the similarities and differences obtained with CHG (now called "with-CHG") and no-CHG materials.

Reviewer:

The authors should document how they "calculated" the eutectic temperature (they would need to know the composition of both the CHG and no-CHG regions in the sample to do so) and whether or not they tried to account for the effect of cooling rate on the eutectic temperature.

Authors:

The composition of the cast-iron is given in the section "experimental details", and it has been verified that it is the same in the CHG and the no-CHG areas (reference #11), i.e. that there is no macrosegregation. The eutectic temperature which is evaluated is that obtained from a phase diagram calculation, denoted "stable eutectic temperature" just above, as described in reference #13. Its value is given in the same paragraph of the section "experimental details".

Reviewer:

The data shown in Figure 3 looks like classic nucleation and growth.

Authors: Certainly, and the stable eutectic temperature gives the upper temperature limit for both nucleation and growth.

Reviewer:

The DTA records that show two phase transformations (Figs 6&7) may simply be a liquidus and solidusthe recalescence that occurs due to undercooling or differences in inoculation. The reported chemistry is near eutectic and the authors did not determine the actual chemistry of their DTA samples. This needs to be clarified.

Authors:

It may be necessary to stress that DTA is not obtained by differentiating a thermal analysis curve. Any peaks on a DTA record such as the two peaks appearing in the eutectic range of this study relate to heat release in the sample. Accordingly, the solidus that is the end of solidification, would not give a peak, though it may possibly be associated to a peak summit.

  RI WKH '7$ VDPSOHV IURP WKH ZLWK&+* DQG QR&+* DUHDV FRROHG DW YDULRXV VFDQQLQJ UDWHV D .PLQ E .PLQ DQG F .PLQ 1RWH WKDW WKH VFDOH LV QRW WKH VDPH IRU E ZLWK&+* DQG E QR&+* DV IRU WKH RWKHU

$FNQRZOHGJHPHQWV

The authors would like to thank the financial support obtained from the Industry Department of the Spanish Government for (ref. PROFIT FIT-030000-2007-94).