Jean-Baptiste Camps

Thibault Clérice

Ariane Pinche

Noisy medieval data, from digitized manuscript to stylometric analysis: Evaluating Paul Meyer's hagiographic hypothesis

Introduction

Understanding the French Hagiographic Tradition

The history of the early French saint's Lives collections in prose is still a mystery. Indeed at the beginning of the thirteenth century, legendiers (i.e. manuscript containing Saint's Lives collection) were already constituted and preliminary steps are missing. In the case where those collections do not adopt the liturgical calendar, they often are built around thematic series (Perrot, 1992:11-15): apostles, martyrs, confessors, saint virgins, but the organization within those themes isn't clear. One of the hypotheses about the composition of hagiographic collections in Latin with similar structure is that they are a compilation of pre-existing libelli, independent units about one saint or a series of saints [START_REF] Philippart | Les Légendiers latins et autres manuscrits hagiographiques[END_REF]. Paul Meyer's1 work on the composition of Old French prose legendiers [START_REF] Meyer | Légendes hagiographiques en français[END_REF] led him to discover that some of these came from successive compilations. Using their macrostructure, he tried to organize French manuscripts into families. The first three collections named A, B and C are composed by successive additions. Thereby, collection A is a collection of saint apostles' Lives, collection B adds a collection of saint martyrs' Lives and collection C is the aggregation of collection A, B and 22 new texts: saint confessors' Lives, saint virgins' Lives, one text about the antichrist and another about the purgatory. New additions to the collection are not united by a thematic object and seem messier. Studying those compilations, Paul Meyer had also the intuition that the collections possess some smaller pieces. He identified a few series using authorship when he could (eg. Li Seint Confessor of Wauchier de Denain in collection C) and proposed the existence of primitive series based on the repetitive grouping of selected lives in different manuscripts as for instance the series: Saint Sixte, Saint Laurent and Saint Hippolyte.

Because most of the French saint's lives are anonymous and because the collections were rearranged by multiple editors over time, it is extremely difficult to locate what could have been the primitive series and Meyer couldn't go further. This serial composition of the Lives of Saints is a datum also noted by other specialists of Latin hagiography such as Perrot (1992) and [START_REF] Philippart | Les Légendiers latins et autres manuscrits hagiographiques[END_REF], who even points out that these hagiographic series must be studied in their entirety in the same way as a literary work. However, despite these academic positions, to our knowledge, there is no complete edition of hagiographic series, most probably because the identification of the series themselves is a matter of debate, except in the context of a full manuscript edition.

As such, the aim here is, first, to determine if Paul Meyer's intuitions and hypotheses can be infirmed, nuanced or completed. Second, we would like to discover if some other links between saint's lives can reveal series from single anonymous authors and help reconstitute some of the hypothetical pre-existing libelli. In order to do so, we performed a stylometric analysis on one representative of the collection C. To perform this computational approach, and because there is no complete edition of any of the manuscripts holding the collection C, we created a pipeline to acquire the text. After the presentation of the data acquisition pipeline, we will explain how we approach the inherent problems of both Old French and OCR variability in our stylometric analysis. Finally, we'll propose an evaluation of the results in regard to the traditional knowledge we have of the manuscript transmissions.

Development and Evaluation of a Data Pipeline

For this work, the BnF fr. 412 manuscript, written in a single hand during the 13th century, seems to be a valid source for text acquisition: it was most probably written in a short time, which does not impact too much writing style (the writer's hand does not "age"), it is in pristine condition and has been digitized by the Bibliothèque Nationale de France (BNF) and made available on Gallica2 . To be able to analyze the text, we had to build a pipeline that would, step by step, enrich the data with more information: from pictures to text, from raw text to normalized version, from normalized version to linguistically annotated data so that multiple stylometrical approaches could be

Line Detection

Handwritten Text Recognition has evolved much over the course of the past years, with easy to use tools such as Transkribus and Kraken. We distinguish two steps of text acquisition: layout detection (and particularly line detection) and the actual text recognition.

As [START_REF] Garz | Binarization-Free Text Line Segmentation for Historical Documents Based on Interest Point Clustering[END_REF] put it, "segmenting page images into text lines is a crucial pre-processing step for automated reading of historical documents" : unlike printed books from modern editions, parchments present various issues from ink bleedthrough (the capacity of a verso writing or picture to be seen on a recto) to inconsistent background color. On top of these traditional issues, costly manuscripts like the BnF fr. 412 accompany texts with illumination, including historiated lettrines, flourished initials and marginal ornamentation, as well as rubrics, underscoring in this way the discontinuity between texts (see Fig. 2).

Line detection was found to perform very poorly in Kraken compared to Transkribus, two well known and performant HTR and OCR engines. Kraken in its 2.0.5 release contains a traditional line segmenter based on contrast which cannot be trained on a specific layout while Transkribus is using deep-learning models for the same work3 . While it should be stressed that we cannot offer a methodical, reapplicable evaluation for this performance, we can definitely say that Kraken would often miss lines, create a lot of false positives in ornamentation, and -not often but enough to be seen -incorrectly sort the lines. On the other hand, Transkribus would rarely miss lines, rarely find text in illuminations (although it could happen), but had some time issues with last lines of columns (see Fig. 3). We believe in subsequent results Kraken output to be much noisier than Transkribus.

HTR

Text acquisition was evaluated using both Transkribus (HTR+) and Kraken. Two datasets have been created for these specific reasons:

1. The main dataset, Pinche Dataset below, is the combination of 271 columns transcribed by A. Pinche, spanning from folio 103r to folio 170v (Pinche, In progress). It has the advantage of having only one transcriber and has been proofread in the context of an ongoing PhD thesis. It contains 96 characters (single spaces included), of which 28 are found fewer than 10 times, and in total makes up to around 495,000 occurrences. However, it has the downside of being both consecutive and attributed to a single author (Wauchier de Denain).

2. ). The downside of this dataset is that it was mostly transcribed by non-specialists and despite several attempts to unify it still presents differences in how the text was transcribed. It contains 102 different characters (single spaces included), of which 46 are found less than 10 times, and in total makes up to around 70,000 occurrences.

We trained 3 models, each of them tested on the same subset of Pinche dataset. As expected, the training set from Pinche was more efficient (most probably due to its single expert transcriber). However, we found Kraken to be quite impacted by the recognition of spaces. As such, we trained a supplementary second model that would not try to recognize spaces. The Transkribus HTR+ model performed best on the Character Error Rate (see Table 1).

Folio 1r-3v were excluded from OCR, because they contain unrelated resources (mostly calendars).

Word Segmentation

As it can be seen in the resulting text (see Fig. 5), spaces are one of the least stable features to be correctly recognized. If spacing in handwriting is rarely really regular, Old French manuscripts are a prime examples of it4 . Indeed, a quick look at one column from the f.10r in Figure 5 shows that spaces are sometimes really small, sometimes non-existent. Moreover, there are no marks for hyphenation in the manuscript, which requires us to detect and concatenate some of the tokens passing from one line to another. As an indication, the Kraken model trained with spaces had 905 errors related to spaces from which 810 were deletions and insertions: it represents a 1.82 point drop of performance in CER and an impressive 37.39% of the test set errors. An option is to treat the notion of space as a natural language processing (NLP) task, where the image is not taken into account. Of course, the notion of words and grammar has evolved and what most of the other tools of the pipeline expect are words perceived as such by modern and contemporaneous medievalists. Unfortunately, due to the extreme variation in spelling of Old French, dictionary approaches do not perform well. In a previous study [START_REF] Clérice | Evaluating Deep Learning Methods for Word Segmentation of Scripta Continua Texts in Old French and Latin[END_REF], we have shown that they do not extend to new unknown domains as much as deep learning models. In this context, we used Boudams, the tool developed for the aforementioned paper. It currently removes all spaces before reinserting new ones. We used the Old French model built for that study, which had a 0.99 FScore on the in-domain test set (which contained resources from the Pinche Dataset and TNAH Dataset) while having a 0.945 FScore on an out of domain dataset.

Of course, the resulting output is not expected to be perfect (see Table 2), and in fact, each step we pursue might introduce new errors as they were not manually transcribed or corrected. However, we did keep the output of each step for later Figure 5: Part of f.10ra. Green lines are measurable space, pink are spaces that are not written, stars represent hyphenation. Transcription with space width in square brackets (for reference, first "a" width is 31px wide), ± 2px: "Entendre la

[4]glorieuse passion[6]saint pierre[0]l[0]apos tre[2]de[4]son martyre[6]q[0]il rechut[6]por nos- tre[6]sigñ si[9]est[0]la[2]ve rite[2]de[0]l[3]escrip".
Largest space in this area represents 35% of the reference a, while smallest measures 6.45% of it. A space is the area available between the furthest right pixel of the left letter and the leftmost one of the next.

Abbreviation resolution, normalization and lemmatization

With word segmentation available, there were two others forms of the dataset that were needed: one where each word would be normalized and have its abbreviations resolved, a second where each word would be tagged with both its Part-Of-Speech and its lemma. We actually treated normalization and abbreviation resolution as a lemmatization task, as they both require understanding of phenomenon such as prefix and suffix and replace them with a neutral value.

As such, we trained Pie (Manjavacas et al., 2019) on a corpus of Old French transcriptions available in TEI5 . The training set was composed of around 125,000 tokens (including punctuation), the evaluation set 16,000 and the test set 15,000 taken from both Pinche and Oriflamms project [START_REF] Stutzmann | Ontology Research, Image Features, Letterform Analysis on Multilingual Medieval Scripts -ORIFLAMMS[END_REF]. They contained abbreviation resolution, accentuation and punctuation introduction (sen -> s'en). The results were promising with 96.86% accuracy, with 96.96% on ambiguous tokens (whose input can be normalized in different fashions), 91.42 % on unknown output form, and finally 90.72 % on unknown origin form.

To improve statistical calculations based on occurrence counts, we applied lemmatization. Unlike modern English, Old French is both defined by its spelling variation (not only between regional scriptae but also inside them), and its rich morphology.

As such, the same word with different flexions can be written in different fashions. In the Pinche Dataset, which represents 27.34% of the whole corpus to be lemmatized in Transkribus6 , the verb avoir (to have) has 57 different spellings, the pronoun il 17, the nouns emperëor 8, the adverb tout (all) 14, the adjective saint 11: eg. "compagnie" can be found written as compagnie, compaignie, compaignies, compaigniez, conpagnie, conpaignie, conpaignies.

Pie is a lemmatizer specifically designed to deal with historical languages with such traits as those found in Old French. We trained a lemmatizer on a dataset of approximately 500,000 lemmatized tokens which were taken from the Chrestien corpus (Kunstmann, 2009), the Geste corpus (Camps, 2019), the Institutes [START_REF] Olivier-Martin | Les Institutes de Justinien en français[END_REF], the Lancelot (Ing, in progress) and the Wauchier (Pinche, In progress) datasets7 . The overall model had 96.38 % accuracy on the test corpus comprised of 48,317 tokens, punctuation included [START_REF] Clérice | Deucalion, Modèle Ancien Francais (0.2.0)[END_REF].

The final result is a lemmatization and pos-tagging of each document. Error accumulation through successive post-processing steps, and noise in the source HTR dataset leads to a dataset with varying quality, although some parts of the document, if not most, are treated with satisfying results.

To evaluate the impact of all pipeline steps on lemmas and POS 3-grams frequencies, in a case where the total number of words can differ, we evaluate the differences with the ground truth followingly, Where tf (A i ) is the absolute term frequency of feature i in document A to be evaluated, and tf (B i ) it's frequency in document B, the ground truth.

∆ A,B = ∑ n i=1 |tf (A i ) -tf (B i )| ∑ n i=1 tf (A i )
We also provide the ratio of hapaxes in A compared to B and vice versa.

Stylometric analysis

The stylometric analysis has to address several challenges, resulting both from the nature of the texts and from the data acquisition pipeline: the short length and anonymity of most texts; the noise in the authorial signal caused by successive errors or innovations in the tradition of the texts (variants) as well as the amount of spelling variation; the noise (and potential biases) resulting from the data acquisition pipeline.

Even though stylometric methods have shown to be relatively resilient to a -simulated or observed -moderate amount of noise [START_REF] Eder | Mind your corpus: systematic errors in authorship attribution[END_REF][START_REF] Franzini | Attributing Authorship in the Noisy Digitized Correspondence of Jacob and Wilhelm Grimm[END_REF], devising a stylometric setup to partially eliminate or circumvent it is still likely to lead to more reliable results.

Unsupervised analysis of short anonymous texts

The texts from the manuscript are, on average, quite short, with a median value of 3,539 words, and extreme values of 298 and 18, 971 (see Fig. 6). Texts that are too short create a problem of reliability, as the observed frequencies may not accurately represent the actual probability of a given variable's appearance [START_REF] Moisl | Finding the Minimum Document Length for Reliable Clustering of Multi-Document Natural Language Corpora[END_REF]. To limit this issue, we removed texts below 1,000 words, a relatively low limit when compared to existing benchmarks [START_REF] Eder | Does Size Matter? Authorship Attribution, Small Samples, Big Problem[END_REF][START_REF] Eder | Short Samples in Authorship Attribution: A New Approach[END_REF], but motivated by the necessity to not exclude too many texts.

Given the short length of the texts and the sparsity caused by noise, we implement a procedure to select for analysis only those features that satisfy a criterion of statistical reliability. In this, we follow the procedure suggested by [START_REF] Moisl | Finding the Minimum Document Length for Reliable Clustering of Multi-Document Natural Language Corpora[END_REF], in the implementation already used by [START_REF] Cafiero | Why Molière Most Likely Did Write His Plays[END_REF]. To summarize it, features are only retained if they match the desired confidence level and margin of error even for the smallest text in the corpus. For each feature (e.g., the function word 'et'), the minimum text size n is calculated with

n = p (1 -p) ( z e ) 2
where p is the mean probability of the feature in our corpus; z, the confidence level, and e, the margin of error. We take z = 1.645 to obtain a confidence margin of 90%, and e = 2σ, where σ is the feature's standard deviation. Beforehand, to correct for normality, we generate a mirror-variable [START_REF] Moisl | Finding the Minimum Document Length for Reliable Clustering of Multi-Document Natural Language Corpora[END_REF]:

vmirror ji = (max v + min v )-v ji
where v j is the vector of the feature j, max v and min v are the maximum and minimum values in v j , and v j i is the relative frequency of j in a sample i. This mirror-variable is concatenated with the original variable in order to compute n. If n is superior to the length of the smallest text in our corpus, we then exclude the feature from further analysis.

Because most of the texts of the manuscript are anonymous, we follow an unsupervised approach to their analysis [START_REF] Camps | Setting Bounds in a Homogeneous Corpus: A Methodological Study Applied to Medieval Literature[END_REF][START_REF] Cafiero | Why Molière Most Likely Did Write His Plays[END_REF], using agglomerative hierarchical clustering with Ward's criterion [START_REF] Ward | Hierarchical Grouping to Optimize an Objective Function[END_REF], guided by its ability to form coherent clusters.

The metric and choices of normalization are also an important parameter, one to which much attention has been devoted [START_REF] Evert | Understanding and explaining Delta measures for authorship attribution[END_REF][START_REF] Jannidis | Improving Burrows' Delta-An Empirical Evaluation of Text Distance Measures[END_REF].

Following the benchmark by [START_REF] Evert | Understanding and explaining Delta measures for authorship attribution[END_REF], we chose to use Manhattan distance with z-transformation (Burrows' Delta) and vector-length Euclidean normalization.

Noise Reduction and Choice of Features

In the form in which they have reached us, medieval texts are noisy by nature, because they contain the successive errors and modifications made by generations of scribes in the successive copies of the works. Moreover, their language is stratified and can contain spellings and other linguistic features originating from the dialect and regional scripta of the successive scribes, creating a very important and heterogeneous spelling variation. The choice of working with the texts of a single manuscript was already guided by the aim of limiting this kind of noise, but is not, in itself sufficient. For this reason, further normalisations, such as abbreviation expansion and lemmatisation, were included in the data acquisition pipeline. Yet, even though it achieves satisfying accuracy at each step, the pipeline itself, through the residual presence of errors, introduces noise as well. Moreover, since the training corpora for each algorithm were not selected by a perfectly random process, they introduce the risk of potential biases.

To handle these risks, we chose to retain raw as well as normalised data for the analyses, using three feature sets: 1) Character n-grams from raw HTR data (baseline);

2) Functors: pseudo-affixes from expanded data, function words and POS ngrams;

3) Words: word forms from expanded data and lemmas.

The aim of feature set 1 is to avoid biases resulting from the pipeline, and for this reason to use the initial raw output of the Transkribus HTR model, excluding all further normalisation steps. Previous research has shown that character n-grams could be a way to circumvent issues due to noisy OCR output, especially when compared with most frequent words [START_REF] Eder | Mind your corpus: systematic errors in authorship attribution[END_REF]. Following existing benchmarks [START_REF] Stamatatos | On the Robustness of Authorship Attribution Based on Character N-Gram Features[END_REF], we choose n = 3 for our character n-grams. Because it fits our case closely, we consider this feature set to be our baseline, and complement it with two others.

Feature set 2 is built to capture functors, i.e. grammatical morphemes (Kestemont, 2014), while circumventing the noise due to scribal variation of palaeographic and graphematic nature. Functors have long been -and often still are -considered the most effective feature for authorship attribution, because they capture unconscious individual variation, while being less dependant on generic or thematic context. In this feature set, we used expanded data to extract pseudo-affixes, i.e. a specific kind of n-gram that has been shown, along with punctuation n-grams, to outperform others [START_REF] Sapkota | Not All Character N-Grams Are Created Equal: A Study in Authorship Attribution[END_REF], perhaps because of its ability to capture grammatical morphemes. Since there is no authorial punctuation in our case, we extracted four kinds of pseudo-affixes n-grams: 'prefix' and 'suffix' (the n first or last characters of words of at least n+1 characters), as well as 'space-prefix' and 'space-suffix' (the interword space with the n-1 characters preceding or following it), with n = 3. For instance, for 'annoncier', we extracted '^ann', 'ier$', '_an' and 'er_'. We also included function-words. Function words are commonly recognised as one of the most effective features (if not the most) for authorship attribution [START_REF] Argamon | Measuring the Usefulness of Function Words for Authorship Attribution[END_REF][START_REF] Koppel | Computational Methods in Authorship Attribution[END_REF][START_REF] Kestemont | Function Words in Authorship Attribution. From Black Magic to Theory[END_REF]. Finally, we added information on the morpho-syntax of the texts, by extracting Part-of-Speech 3-grams such as 'PRE DETdef NOMcom' (preposition, definite article and noun, e.g. 'a la corone'). POS 3-grams have sometimes shown to be a quite effective feature for cross-topic authorship attribution [START_REF] Gómez-Adorno | Document Embeddings Learned on Various Types of N-Grams for Cross-Topic Authorship Attribution[END_REF]. In this case, multiplying the measurements by concatenating three types of features in this set is done to help deal with short noisy texts and improve reliability.

Feature set 3 is constituted because -despite the broad consensus on the use of functors -some recent studies seem to advocate the use of longer word lists as a feature for authorship attribution [START_REF] Evert | Understanding and explaining Delta measures for authorship attribution[END_REF]. Using words forms is, in our case, both interesting, because it allows us to retain morphological information, and risky, due to the extent of spelling variation, attributable to the scribes. To account for that, we also include lemmatized words, which, in turn, are dependent upon the accuracy of the lemmatizer.

Results and Cross-Validation

The results on the three feature sets are included in fig. 7 HC1. Our baseline result (see Fig. 7 HC1,top) is also the one closest to Meyer's classification, often up to the ordering of the texts, though displaying a few differences (6 out of 59 texts, concerning mostly texts of B included with C). The results on feature sets 2 and 3, though keeping the same macrostructure, display some interesting variations with the inclusion of a mixed B/C subgroup within Meyer's A.

In order to get more insight into feature sets 2 and 3, we also give supplementary results on their components (see Fig. 8 HC2). This can be useful since differences on clusterings based on separate aspects (e.g. morpho-syntactic sequences vs. function words or affixes) could reflect differences in groupings when alternative perspectives are taken on the language; or punctually yield useful information on some texts, as we vary the lens with which we observe it.

In order to check the robustness of our results, we give, for each analysis shown in fig. 7 HC1 and fig. 8 HC2,four indicators: • The number of analysed features and the agglomerative coefficient, that, taken together, give an indication of the quality of the clustering;

• The cluster purity of the groups (with k = 5) as compared with Meyer's Hypothesis on A, B and C, and Wauchier's alleged texts; Meyer), cluster purity when compared to the baseline

• The cluster purity of the groups when compared to our baseline (results on feature set 1).

These figures are given in table 7. [START_REF] Eder | Short Samples in Authorship Attribution: A New Approach[END_REF] showed that, whatever the variation of sample length, some texts were never correctly attributed (at least when a given feature set is used) and suggested to measure the diversity of attributions of individual texts -what we call volatility -to help identify these cases when the authors are not known. Following this, one could hypothesize that the presence of classification resistant (or volatile) texts is to be expected in a sufficiently large corpus.

To measure the volatility of any individual text, in the context of unsupervised analysis, we wish to measure the stability or volatility of its neighborhood. We devise a specific metric V i that aims to compute the volatility of the neighborhood of a specific text i in the groups of which he is a member in all the clusterings performed. Let (G j ) j∈J,i∈G j be the family of sets of which i is a member, where J is the total number of clusterings performed. We can then construct a set X, containing all unique texts {x a . . . x n } occurring in at least one set of the family (G j ), X = {x|∃j ∈ J, x ∈ G j }. For each x, the family (G j ) can be split in two subfamilies, (A k ) k∈J,x∈A k and (B l ) l∈J,x̸ ∈B k . We then compute a global volatility index as follows:

V i = ∑ n a=1 card(A k ) k∈J,xa∈A k -card(B l ) l∈J,xa̸ ∈B l card((G j ) j∈J )

card(X)

Since we normalize it by the total number of elements in X, this index is limited by [-1; 1], where -1 would indicate a perfect volatility (all sets with no member in common) and 1 perfect stability (all sets with the same members). 8: For each text, its number of words, and volatility index (V) based on the three reference analyses (V Ref ) or the supplementary analyses (V Suppl). Texts are sorted on V Ref in increasing order

The results of this procedure are given in table 8. We notice that the texts attributed to Wauchier are the least volatile, while there is a small group of volatile texts achieving a score < 0.5.

Another indication yielded by this index is that volatility is not (or almost not) due to variation in sample length (See Fig. 9). The small relationship, on the edge of Figure 9: Scatterplot and regression lines for V ~NWords, for both reference analyses and supplementary analyses significance, between text length and volatility that we observe when looking only at the supplementary analyses disappears totally when we look at the reference analyses. This could be an indication that the strategy we have adopted, of concatenating several measurements to increase reliability on short texts, is working.

Controlling for pipeline bias

To control for the presence of bias due to the training data used by the pipeline, we perform the same set of analyses on the data obtained with models trained on alternate data (TNAH corpus) or with different tools (Kraken), and compare it with our analyses displayed above. The results are displayed in table 9. Even though the models achieve quite different accuracies, the results are not significantly different, and show a particular stability on the three main analyses (mean CP of 0.95 and 0.92, table 9). The results based on a change of training corpus are actually closer than the one obtained with the same corpus but a different HTR software, though the difference remains small.

Interpretation of the results

The manuscript fr. 412 allows us to control the results of our approaches by checking the unity of the Wauchier de Denain collection8 in the stylometric trees. On the three reference analyses (see Fig. 7 HC1), the Wauchier group, with the adjunction of the Life of saint Lambert, is the most clearly distinguished group. This same configuration, with or without Lambert, is also visible on all supplementary analyses, except the ones based on POS 3-grams and lemmas (see Fig. 8 HC2). These two analyses also achieve low agglomerative coefficient, given their number of features, and low cluster purity, both in comparison with Meyer's classification and with our baseline; facts which advocates for considering them as outliers, with low reliability. Moreover, in their globality, the results seem to agree with Meyer's hypothesis, with CP from 0.83 to 0.9 for the reference analysis (0.71 to 0.85 for the others, see Table 7). This is particularly obvious for our baseline (see Fig. 7 HC1, top, reproduced here as Fig. 10), that represents the manuscript fr. 412 as a successive Figure 10: Results on char. 3-grams from raw HTR data, with indication of the successive collections addition of collections A, B and C, which appear in separated branches. This can also be observed in the other trees, even if in a slightly noisier fashion. For this reason, Paul Meyer's hypothesis seems to be confirmed by our results. Nonetheless, they can be nuanced or made more accurate in a few cases, as we will see. A subgroup mixing texts from Meyer's B and C can be observed in our results (see Fig. 7 HC1). It contains Saint Catherine Life,Saint Andrew Life and Miracles,, as well as the Assumption of Our Lady and, but not always, Antichristi (n. 42 and 60)9 . In the trees, this subgroup is sometimes included in C, sometimes in A. The Assumption and the Antichristi were identified by Paul Meyer as texts from collection B and the second one was assumed to have certainly been published first in an autonomous way with some others texts : Saint Patrice's Purgatory, Julian and Brendan Lives (Meyer, 1906:405).

Volatile texts and exceptions to Meyer's classification

Clément and Patrice

Clément and Patrice are integrated in collection C (as opposed to Meyer's B) in almost all analyses. A precise interpretation of this remains to be found, but one can note that, Patrice has been supposed by Paul Meyer as having been published first as part of a preexisting libelli and autonomously from collection B (or C) with Antechristi.

However, given the very small amount of texts erratically classified, and given the pre-existing difficulties faced by Paul Meyer concerning some of these, we do not expect this to contradict our former conclusion. The apparent volatility of Marc and Jacques can partially be disregarded, as they appear to only switch subgroups while remaining inside A.

Collection A

Paul Meyer identified collection A as a group of twelve texts. It is most apparent on the baseline analysis (see Fig. 7 HC1, top). From our results, it can be refined in two subseries A1 and A2 (see Table 10) . Thematically, this regroupment makes sense. On one side, we find major apostles, creators of Christian Church, with two sequences of three and two texts following each others. On the other side are minor apostles which do not present sequences in theme or the likes.

To conclude about the collection A, in contrast to Meyer's hypothesis, Saint Longin Life is almost never grouped with any of the aforementioned series, but is nearby, being clustered as the first element of B.

Collection B

Collection B contains nineteen texts, thematically centered around martyrdoms. Of those, sixteen are sequentially found in MSS BnF fr. 412, the three others being study cannot determine the order of apparition.

Finally, Paul Meyer, during his work about the different hagiographic collections, has seen that, in the collection B, the series Sixte-Laurent-Hippolyte was frequent in the manuscript tradition (Meyer, 1906:495). This reunion appears in our three analyses. Furthermore, the dendrogram based on function words (see Fig. 8 HC2, top-right) links Laurent and Hippolyte with Pantaleon. This addition isn't in contradiction with the tradition: collection G13 contains them sequentially in three of its four witnesses, and in collection C (three manuscripts) saint Pantaleon's Life is only separated by Saint Lambert's Life from the other ones. As such, it is possible that their gathering confirms a predating series.

Collection C

Collection C contains twenty-two texts without any apparent major theme. Collection C seems to have two major series, one constituted by Wauchier de Denain's Seint Confessor, and the other one containing all the others texts.

First, we can see that the Lives of Saint Maur and Placide and Saint Benoit's Translation 15 form a series C2. The translation and the Life of saint Maur are grouped in our three analyses, and the Life of Saint Placide is also close to or part of the group. Those Lives have a thematic unity: the translation of the body of Saint Benoit, followed by the Lives of his disciples, Saint Maur and Saint Placide.

Another series C3 appears in all three analyses (see Fig. 7 HC1): Saint Marguerite, Saint Pelagie, Saint Euphrasie and probably also The Life of Saint Mary the Egyptian. Surprisingly, we can extend this series to a subseries C3b containing one, perhaps two, men's lives: the Life of Saint Mamertin, always present as well, while the Life of Saint Simeon is more punctually associated with this group, when considering only function words or function lemmas.

Finally, this study has revealed an astonishing rapprochement between Li seint Confessor and the Life of saint Lambert. Normally, Saint Lambert's Life is part of collection B, but following our preceding analysis, Saint Lambert's doesn't fit in any group of the collection. In fact, we have to look at some of the supplementary analyses to find results where it is not associated with Wauchier's works (POS 3grams, function lemmas, and lemmas, Fig. 8 HC2), all potentially influenced by the nature of the training corpus. However, from a close reading perspective, it's difficult to affirm the authorship given the fact that Saint Lambert Life does not possess any of the usual distinctive marks of Wauchier de Denain's style such as verses in prose, signatures or vernacular translation of Latin citations. Moreover, there is no references to Philippe of Namur, Jeanne of Flanders or Roger squire of Lille, Wauchier de Denain's patrons. There is also no evident Latin common substrate between the lives of Li Seint Confessor and Saint Lambert Life. The only common point which can be found is in the localization and the theme. Liege is close to the Namur area16 Saint Lambert is an important saint, a bishop linked to power, having contact with Pepin, king of the Franks. The chosen version is the one with a positive representation of royal power. So, we are in the presence of a bishop, ally of power, like Saint Martin or Saint Martial. On the other hand, one possible hypothesis regarding a potential Wauchier's authorship is that Saint Lambert Life is an early text, where the author erases himself and stays in the role of a simple translator. Consequently, without any easy proof of classification, further study of Saint Lambert Life's relationship with Wauchier's work should be done.

Conclusion and further research

In this paper, we offer a complete pipeline to acquire and analyse medieval data, using a hybrid approach of human and artificial intelligence. Using machine learning, we are able to acquire and process textual data from medieval manuscript images, and then submit it to a stylometric analysis setup that seems able to deal with noisy data. The application of this procedure offers perspectives for ancient or medieval Cultural heritage data, and could be extended to other material.

From a methodological and stylometric perspective, the challenge was, in a context where supervised analysis was not an option, to deal with short texts, whose data was noisy in two regards: first, because of the noise generated during text recognition (HTR) and further processing steps; second, because of the noise inherent to medieval data (spelling variation, variants, etc.). From our observations, our baseline that involved character n-grams with raw HTR data (already suggested as the most adapted to noisy OCR or HTR data in previous studies) can still be considered a very efficient procedure. Our attempts to suppress noise due to spelling variation by using other types of features such as lemmas or POS 3-grams, though offering alternative insights into the data, do not seem yet able to surpass it significantly, perhaps because of the cumulative error rates for each processing step. On the other hand, concerning the shortness of the texts, our results seem to agree with the notion that it is possi-ble to analyse texts below 3000 words; more specifically, by using less sparse features, such as characters 3-grams, or by concatenating different features, different views on the same text, we seem to achieve stable results, independent of the variation of sample length in our corpus.

From a thematic perspective, on the whole, our results confirm (or fail to disprove) Meyer's hypothesis regarding the constitution of Old French legendiers. They also bring to light some new facts, such as potential subseries that were not previously identified, and raise questions about Saint Longin's life, that, we believe, can be considered part of collection B instead of A, and the life of Saint Lambert, whose possible attribution to Wauchier de Denain is deserving of further investigation.

Finally, we hope that our approach can motivate new investigations, using computational humanities, on philological and historical holistic hypotheses formulated in the 19th century, that still sometimes form the basis of our understanding of the sources. By bringing together the work of the founders of our fields, such as Paul Meyer, and novel computational methods, we can hope to achieve progress in many areas, and perhaps more specifically in those that are left out of the literary canon envisioned by many close reading studies.

Figure 1 :

 1 Figure 1: Representation of the possible composition of French hagiographic collections based on Paul Meyer's hypothesis

Figure 2 :

 2 Figure 2: Examples of manuscript layout issues for line segmentation: ink bleedthrough and disappearance of text (bottom left), flourished and highlighted initials (second column from the left, both top and bottom), historiated initials (third column), litterae elongatae on first and last lines (last column) from fol.9r and fol.10r

Figure 3 :

 3 Figure 3: Line detection in both Transkribus (first and second from the left) and Kraken. White areas are marked as lines. In these examples, we can see the illumination incorrectly identified as text (much more important in Kraken that in Transkribus), the false negative on the last line in Transkribus and various issues in Kraken in general.

Figure 4 :

 4 Figure 4: Distribution of character counts

Figure 6 :

 6 Figure 6: Boxplot of text lengths in words, based on the Transkribus + Boudams data

Figure 7 :

 7 Figure 7: HC1: Main results from agglomerative hierarchical clustering (Ward's method, Manhattan distance with z-scores and vector-length euclidean normalisation) on the three feature sets (top, character n-grams from HTR data; middle, functors; bottom, word forms and lemmas).

Figure 8 :

 8 Figure 8: HC2: Supplementary results from agglomerative hierarchical clustering (identical setup) on the components of feature sets 2 and 3 17

Table 1 :

 1 Character error rate based on software and corpora

	Engine

Table 2 :

 2 Example of results and ground truth after and before word segmentationTranskribus Raw entendre la glorieuse passion saint aun piere lapos stre de son . martyre q'il rechut por nostre signor : si est la ve rite del escrip ture Transkribus + Boudams entendre la glorieuse passions aint a un piere la posstre de son . martyre q'il rechut por nostre signor : si est la verité del escripture Kraken (No Space) + Boudams entendre la glorieuse passions art piere la positre de son . mantyere q'il rechut por nostre signor : si est la verité del escriptire Correct Entendre la glorieuse passion saint piere l apostre de son martẏre q il rechut por nostre signeur si est la uerite de l escripture

Transkribus

Entendre la glorieuse passion saĩt aun piere lapos stre de son. " martẏre qil rechut por nostre sign: si est la ue rite del escrip ture Transkribus + Boudams Entendre la glorieuse passions aĩt a un piere la posstre de son ." martẏre qil rechut por nostre sign : si est la uerite del escripture Kraken (No Space) + Boudams Entendre la glorieuse passions aͣ t piere la positre de son . mantẏre qil rechut por nostre sign : si est la uerite del escriptire Correct

Entendre la glorieuse passion saït piere l apostre de son martẏre q il rechut por nostre sign~si est la uerite de l escripture

Table 3 :

 3

Example of results and ground truth after and before abbrevations resolutions resolution stylometric analyses.

Table 4 :

 4 Test scores of Pie over Old French

Table 5 :

 5 Automatic tagging of the OCR text by Pie and ground truth

Table 6 :

 6 Difference between the Gold corpus from Pinche dataset and the HTR results at the end of the pipeline (HTR/Boudams/Pie/Pie). We provide deltas for all values, function lemmas, and Moisl's (cf. below). Specific entries are the relative accumulation of frequencies of lemmas that are found in one version of the corpus but no the other.

				Lemmas		POS 3-gram
			Delta	Specific entries	Delta	Specific entries
	Corpus	All	Function Moisl OCR Gold	All	Moisl OCR Gold
	Martin (29, 30)	33.35	10.69	11.43 34.01 16.92	44.8 32.28 29.59 24.23
	Dialogues (31)	29.38	9.77	9.99 33.01 19.69 48.38 35.85 29.84 23.49
	Brice (32)	39.49	12.14	16.56 29.53 21.39 66.09 47.51 30.95 30.86
	Gilles (33)	32.24	9.83	11.07 25.42 16.91 46.38 34.03 25.56 23.64
	Martial (34)	28.26	7.92	9.68 37.36 21.63 50.29 39.09 30.09 24.83
	Nicolas (35, 36, 37) 29.44	9.33	10.02 38.76	21.8	47.19 35.42 31.42 24.27
	Jerome (38)	34.13	12.59	14.38 19.53 15.12 61.92 52.07 28.66 28.06
	Benoit (39)	27.97	9.64	11.93 30.98 17.74 52.88 44.09 30.88 24.22
	Alexis (40)	30.19	10.65	11.58 21.83 13.17 57.71 47.77 30.16 26.73
	Total	27.76	9.02	9.76 51.57 29.18 43.46 34.90 32.65 21.81

Table 7 :

 7

	N	AC CP Meyer CP Ref

Number of analysed features (N), agglomerative coefficient (AC), cluster purity of the clusters (k = 5) when compared to Meyer's hypothesis and Wauchier's known texts (CP

Table 9 :

 9 Cluster purity of the analyses replicated using models trained on the TNAH corpus or with Kraken, with regard with the analyses presented in fig.7HC1 and fig.8 HC2

		TNAH corpus Kraken model
	Feature Set 1
	Raw 3-grams	0.93	0.90
	Feature Set 2
	Affixes	0.90	0.92
	Function Words	0.83	0.73
	Function Lemmas	0.78	0.71
	POS3gr	0.81	0.88
	FW + POS 3-grams + Affixes	0.98	0.92
	Feature set 3
	Forms	0.84	0.90
	Lemmas	0.84	0.73
	Words + Lemmas	0.95	0.95
	Geom. mean Main analyses	0.95	0.92
	Geom. mean Suppl. analyses	0.83	0.81
	Geom. mean all	0.87	0.84

Paul Meyer (1840-1917) is one of the most famous French romance philologists. He's the author of the chapter about French hagiographic Lives in the book Histoire littérairede la France (1906).

Manuscript BnF fr. 412 on Gallica : <https://gallica.bnf.fr/ark:/12148/ btv1b84259980/>.

It should be noted that Kraken main developer, Benjamin Kiessling, is working on implementing learnable layout analysis (cf. https://github.com/mittagessen/kraken/issues/155).

However, it is not a specific handwriting issue, but more a question of what was space and words at the time. On this subject, see[START_REF] Stutzmann | Words as Graphic and Linguistic Structures: Word Spacing in Psalm 101 Domine Exaudi Orationem Meam[END_REF]. Moreover, there is a strong difficulty in appreciating the difference between the intent of the scribe and what we perceive of it(Careri et al., 2001: XXXVII).

We used a model on version 0.2.3 ( https://github.com/emanjavacas/pie/releases/tag/v0.2.3 ).

In the transkribus dataset, Wauchier counts for 122,000 tokens over 446,900 for the whole treated part of the manuscript.

The lemmata are taken fromTobler, A., and Lommatzsch, E. (1952). Altfranzösisches Wörterbuch. E. Steiner.

The collection contains the nine following texts : Saint Martin Life, Sulpicius SeverusDialog, Saint Brice, Saint Gilles, Saint Martial, Saint Nicolas, Saint Jerome, Saint Benoit and Saint Alexis Lives.

Antechristi is only 1346 words long, which is one of the smallest size of the corpora, and below the first quartile. One could hypothesize that the Jugement (61) could function with Antechristi, but this text was excluded because it is below the

words limit. 10 This text is amongst the one removed due to length below 1000 words.

In the manuscript tradition ( we check 18 manuscripts from Li Seint Confessor tradition) there is a really strong link between Agatha and Lucy Lives which appear together in 11 manuscripts, against 7 witnesses where they appear separated in which only two manuscripts have both Lives.

Manuscript BnF fr. 412, fol. 72v.

Bruxelles, Bibliothèque royale, 9225, Paris, BnF, fr. 183, Paris, BnF, fr. 185. 15 The Translation of Saint Benoit is not attributed to Wauchier neither by Paul Meyer nor by our stylometric analysis. Moreover, it is separated from the Life in MSS fr. 412 by 8 others texts.

Indeed Wauchier de Denain comes form the North of France and worked under the patronage of the court of Flanders.

We can observe a strong group composed of twelve Lives: Christophe, Agatha, Lucy, Agnes, Felicity, Christine, Cecile, Sixte, Laurent, Hippolyte and Pantaleon Lives are clearly gathered (see Fig. 7 HC1). We can add to them Georges, Vincent and Sebastien Lives, but saint Clement Life is always missing. Thus, globally, the sequence of the manuscripts is reflected in the classification.

Moreover, in all the selected trees, the Life of Saint Longin classified as A by Paul Meyer is gathered with texts from collection B. Furthermore, thematically, Saint Longin's Life isn't coherent with a series of saint apostles, given the fact that he is a martyr. In manuscript BnF fr. 412, given the order of the compilation, we can considerate Saint Longin Life as the last text of collection A or as the first of collection B. Looking at the manuscripts tradition, in fact this life is mixed with the apostle lives just once in the manuscript BnF, nouv acq. fr. 23686, which happened to be the one Paul Meyer used as his prime material for studying collection A. So regarding our results and manuscript tradition, it seems more accurate to classify this life to saint Martyrs within collection B.

In the light of this hypothetical classification, we can observe two subcollections: A micro-series B1a is composed by Saint Longin, Saint Sebastien, Saint Vincent, Saint Christopher Lives.

Additionally, in B, a micro-series B1b of saint women Lives appears : Saint Agatha, Saint Lucy, Saint Agnes, Saint Christine and saint Cecile. Those Lives are about virgins and also close in the manuscript tradition: the first three texts of the series are often gathered together, as are the last three. There are also textual links between them. One explanation for the proximity between Saint Agatha and Saint Lucy can be the fact that the last seems to be in the continuation of the first's story 11 . Indeed, at the end of her story, Lucy defines herself as an heir of Agatha:

Aussi com la cites de Cathenense est secorue et aidie par seinte Agathe ma seror, aussi sera ceste citez aidie et socorue par moi, se uoz auez foi et creance en nostre Signor 12 .

Just as the city of Catania was rescued by the help of St. Agatha, my sister, this city will be rescued by my help, if you have faith in our Lord.

We can add that both of them come from Sicilia: Agatha from Catania and Luce from Syracuse. There are also some links between the Lives of Saint Lucy and Saint Agnes. The Life of Agnes starts at Rome where the Life of Saint Lucy stopped and they both have to face the threat of a spurned lover who wants to send them to a brothel. We can also note that saint Christine, as saint Agatha, is one of the four patrons of Palermo in Sicilia and that the thematic of the snatched breast, iconic for saint Agatha, can also be found in saint Christine's Life. The reason behind the adjonction of saint Cecile is more obscure: there might be a redundant theme around family and conversion. Finally, we can add that the Lives of this group are amongst the least volatile in our corpus after the Wauchier de Denain collection (see Table 8).

However, both micro-series B1a and B1b can be grouped together as a collection B1 in five of the selected trees. The rapprochement seems logical from the point of view of literary construction because it builds a collection with, on one side, five Lives of men martyrs, and on the other side, six Lives of women martyrs. A stylometric


Patricia Bolle

Nicolas Albrecht

Thibault Amiaud

Bernard Humbert

Eric Faulques

Remi Dessapt

Hélène Serier-Brault

New Robust Luminescent Supramolecular Assemblies Based on [Ln(Mo 8 O 26 ) 2 ] 5-(Ln = Eu, Sm) Polyoxometalates

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

5-complexes in acetonitrile solution has been evidenced by FT-Raman and PL spectroscopies.

Then, the tetraphenylphosphonium (TPP) 5 [Ln(Mo 8 O 26 ) 2 ] derivatives were obtained by a salt metathesis reaction. The two series exhibit a high thermal stability in air and are efficient solid-state phosphors at room temperature.

Polyoxometalates incorporating Ln

3+ lanthanide ions (Ln-POMs) form a fascinating class of nanosized metal-oxide clusters of early transition metals (M = Mo, W, V).

1 They are currently the focus of intense researches owing to their promising applications in the fields of single molecule magnets (SMMs), [START_REF] Aldamen | Mononuclear Lanthanide Single-Molecule Magnets Based on Polyoxometalates[END_REF] catalysis, [START_REF] Boglio | Lanthanide complexes of the monovacant Dawson polyoxotungstate [alpha1-P2W17O61] 10as selective and recoverable Lewis acid catalysts[END_REF] and especially photoluminescence (PL).

4 Na 9 [EuW 10 O 36 ]xH 2 O (EuW 10 ) has been extensively investigated due to its remarkable PL properties [START_REF] Blasse | The luminescence of some lanthanide decatungstates and other polytungstates[END_REF] which were recently used to elaborate chemical probes for biology, 6 photocatalysts 7 and luminescent thermometers. [START_REF] Salomon | A multifunctional dualluminescent polyoxometalate@metal-organic framework EuW10@UiO-67 composite as chemical probe and temperature sensor[END_REF] In the Weakley-type [Eu(W 5 O 18 ) 2 ]

9-complex, the POM ligands act as sensitizers to exalt the luminescence of the Eu 3+ ion via an antenna effect. [START_REF] Blasse | The luminescence of some lanthanide decatungstates and other polytungstates[END_REF] [Eu(W 5 O 18 ) 2 ] 9-has been a l s o ionically incorporated into organic polymers, [START_REF] Wang | Chemically responsive luminescent switching in transparent flexible selfsupporting [EuW10O36] 9--agarose nanocomposite thin films[END_REF] vesicles, 10 surfactants, [START_REF] Zhang | Organized Nanostructured Complexes of Polyoxometalates and Surfactants that Exhibit Photoluminescence and Electrochromism[END_REF] ionic liquids, [START_REF] Yan | Co-assembly and luminescence tuning of hybrids with task-specified ionic liquid encapsulating and linking lanthanide-polyoxometalates and complexes[END_REF] and metal-organic frameworks 8 to design hybrid organic-inorganic photoactive composites. However, because of its huge negative charge and the insolubility of EuW 10 in most of non-aqueous solutions, the assembly of [Eu(W 5 O 18 ) 2 ] 9-with organic cations into crystallized supramolecular frameworks is more critical and was very rarely reported. [START_REF] Shen | A durable and fast-responsive photochromic and switchable luminescent polyviologen-polyoxometalate hybrid[END_REF] Other Eu-POMs were since designed, 4c,5,14 but they are less efficient emitters than EuW 10 because i) they contain corner-shared MO 6 octahedra that favor the electron-to-hole recombination into the POM ligands instead of POM-to-Eu 3+ energy transfers, ii) the Ln 3+ ions are too close to each other leading to PL concentration quenching effects or iii) water molecules link the Eu 3+ ions and promote non-radiative deactivation from its 5 D 0 emitting level. [START_REF] Yamase | Crystallographic characterization of the polyoxotungstate [Eu3(H2O)3(SbW9O33)(W5O18)3] 18and energy transfer in its crystalline lattices[END_REF] In addition, most of these compounds are hydrated alkali salts which exhibit a limited thermal stability. Thus, the discovery of Ln-POMs with lower charges, and soluble in non-aqueous solvents is still highly challenging. In 1997, Kitamura et 5-complex (Ln = La, Y, Ce Pr, Nd, Gd, Yb) (Figure 1a). [START_REF] Kitamura | β-Octamolybdate as a Building Block. Synthesis and Structural Characterization of Rare Earth-Molybdate Adducts[END_REF] Other Ln-derivatives (Tb, Dy, Ho, Er, Tm)

were recently obtained which exhibit interesting SMM properties. [START_REF] Baldoví | A single ion magnets based on lanthanoid polyoxomolybdate complexes[END_REF] However, crystals of these efflorescent acetonitrile solvates degrade rapidly in air, leading to structurally uncharacterized powders. In addition, the photophysical properties of these Ln-POMs have never been investigated, and their Eu and Sm counterparts have not been designed yet.

We report herein the synthesis a n d s t r u c t u r a l c h a ra c t e r i z a t The syntheses of the six compounds are described in the Supporting Information. T h e T B A -L n M o 16 s y s t e m s were obtained as colorless crystals by slightly modifying the synthesis route developed for other Ln-derivatives. [START_REF] Baldoví | A single ion magnets based on lanthanoid polyoxomolybdate complexes[END_REF] Our synthetic procedure also differs from that previously reported for TBA-YMo 16 . [START_REF] Kitamura | β-Octamolybdate as a Building Block. Synthesis and Structural Characterization of Rare Earth-Molybdate Adducts[END_REF] FT-IR spectroscopy (Figure S1), TGA measurements (Figure S2

( T B A ) 5 [Ln(Mo 8 O 26 ) 2 ]
. Noticeably, crystals are stable in air, and no efflorescence appears even after several months. Powder X-Ray diffraction (PXRD) analysis shows that the three compounds are isostructural (Figure S3). The structures of TBA-EuMo 16 and TBA-SmMo 16 were resolved by singlecrystal X-ray diffraction (Table S1), and that of TBA-EuMo 16 is described below. In

[Eu(Mo 8 O 26 ) 2 ] 5-, two -[Mo 8 O 26 ]
4units connect a central Eu 3+ ion (Figure 1a) which is located into a distorted square antiprismatic site. Supramolecular {(TBA) 2 [Eu(Mo 8 O 26 ) 2 ]} 3-ribbons run along the a axis (Figure 1b) with long intermolecular EuEu distances of 12.1 Å and 13.4 Å. Ribbons are separated by TBA units (Figure 1c) with the shortest inter-ribbon EuEu distance of 17.2 Å. As suspected, the structures do not show any crystallized acetonitrile molecules. This is consistent with the absence in the Raman spectra of the i n t e n s e (CN) stretching mode around 2260 cm -1 (Figure S4). [START_REF] Abramczyk | The correlation between the phase transitions and vibrational properties by Raman spectroscopy: liquid-solid β and solid β-solid α acetonitrile transitions[END_REF] In addition, TGA measurements (Figure S2) confirm the stability of compounds in air up to 275°C.

FT-Raman spectroscopy is a powerful tool to characterize POMs in solution and in the solid state.

19 5-match with those recorded for the TBA-EuMo 16 solid phase. In this concentration range, no additional signals that could indicate its partial degradation are observed. Moreover, the intensity of the main line at 977 cm -1 attributed to the terminal Mo=O bonds increases linearly with the Eu-POM concentration (Figure S6). In addition, a statistical analysis by "separation curve method" reveals that the spectra recorded in solution are perfectly similar to the solid one. This quantitatively confirms the integrity of the Ln-POM complex in solution. Then, by exchanging TBA cations by TPP ones, TPP-LnMo 16 (Ln = Eu, Sm) and their Y 3+ counterpart were prepared as microcrystalline powders. Attempts to isolate single-crystals were unsuccessful. However, PXRD analyses show that they are isostructural (Figure S3). Finally, FT-IR (Figure S1) and FT-Raman (Figure S7) spectroscopies, elemental analyses, and TGA measurements (Figure S2) i n d i c a t e a T P P : Ln-POM ratio of 5 : 1, and show that the compounds are thermally stable in air up to 355°C.

The solid-state absorption sp ectra of the TBA-LnMo 16 series (Figure S8) show two broad bands at 270 and 305 nm, which are assigned to mixed OMo and OEu ligand-tometal charge-transfer (LMCT) transitions. Similar bands are observed for the TPP-LnMo 16 series, with a more intense transition at 270 nm, because the cation absorbs at this wavelength. The six compounds have an optical band gap of 370 nm. In addition, room-temperature time-resolved PL spectroscopy has been performed to characterize the intrinsic luminescence of the POM ligands. Upon photoexcitation into the OMo LMCT band, the Ln-free reference TBA-YMo 16 shows a broad emission band centered at 385 nm (Figure S9) with a short mean luminescence lifetime of  = 0.382 s (Table S2). This band can be decomposed into two contributions at 364 (27473 cm -1 ) and 418 nm (23923 cm -1 ) (Table S2). Comparable emissions are also observed for the TBA-LnMo 16 (Ln = Eu, Sm) compounds and their TPP counterparts (Figure S9), with similar decay times (Table S2). Based on earlier studies, 1c,4c these bands have been assigned

to the 3 T 1u  1 A 1g transitions originating from the two OMo LMCT emitting triplet states of the POM ligands. The room-temperature steady-state photoluminescence excitation (PLE) and emission spectra of TBA-EuMo 16 and TBA-SmMo 16 are depicted in Figure 2. Upon irradiation at 254 nm with a standard UV lamp, TBA-EuMo 16 exhibits a strong orange-red emission (Figure 2a). Its PLE spectrum monitored at 594 nm shows a broad intense band at 286 nm (34965 cm -1 ) which corresponds to the charge-transfer states (CTS), mainly dominated by the 1 A 1g  1 T 1u transition of the OMo LMCT photoexcitation.

4c Several sharp lines are also observed which are characteristic of the intra-configurational f-f transitions of Eu 3+ i.e., 4-ligands are effective light-harvesting antennae to sensitize the Eu 3+ ion through an intramolecular energy transfer from the 3 T 1u excited levels to the emitting 5 D 0 level, lying at a lower energy (Figure S10). Upon photoexcitation into the CTS band, the PL spectrum of TBA-EuMo 16 consists in a multi-band emission characteristic of the 5 D 0  7 F J (J = 0-4) transitions of an Eu 3+ ion occupying an asymmetric site with approximate D 4d symmetry. [START_REF] Blasse | Luminescence from the Eu 3+ ion in D4d Symmetry[END_REF] Indeed, the symmetry-forbidden 5 D 0  F 4 split-band (692 and 701 nm) is intense. Thus, the emission of TBA-EuMo 16 is characterized by CIE chromaticity coordinates of (0.6255, 0.3681) (Figure S11). The 5 D 0  7 F 1 transition exhibits a long luminescence lifetime of 5.24 ± 0.03 ms (Figure S12). Noticeably, the emission spectrum of TBA-EuMo 16 shows the same feature than that of EuW 10 and their PL performances are close. 5-and [Eu(W 5 O 18 ) 2 ] 9-have some structural similarities. Indeed, they contain POM ligands only built upon edge-shared MO 6 octahedra that discriminates against thermally activated hopping of d 1 electrons and limits the MO non-radiative deactivation processes.

22,4c They also exhibit low average M-O-Eu bond angle values (131.3° and 130.17° for TBA-EuMo 16 and EuW 10 , 21 respectively). This contributes to prevent the PL quenching of Eu 3+ due to d 1 electron hopping through f-p-d orbital mixing, which is rather favored for higher bond angle values. 4b,c Moreover, the Eu 3+ ion occupies a similar distorted square antiprismatic site without coordinated water molecules likely to quench its luminescence.

22 Finally, the long EuEu distances, higher than 12 Å, may suggest that side PL concentration quenching effects should be strongly minimized. The orange emission of TBA-SmMo 16 at room temperature is less intense than that of TBA-EuMo 16 (Figure 2b). The PLE spectrum contains the CTS band (286 nm) and sharp lines associated to the f-f transitions of Sm 3+ , i.e. ). [START_REF] Kodaira | Photoluminescence behavior of the Sm 3+ and Tb 3+ ions doped into the Gd2(WO4)3 matrix prepared by the Pechini and ceramic methods[END_REF] Its emission color is more orange than for TBA-EuMo 16 with CIE chromaticity coordinates of (0.5841, 0.4065) (Figure S11). The decay time of the 4 G 5/2  5 H 7/2 emission ( exc = 286 nm) is 0.28 ± 0.01 ms (Figure S12). 16 and TBA-SmMo 16 dissolved in acetonitrile exhibit an orange luminescence at room temperature (Figure S13). The PL spectrum of [Sm(Mo 8 O 26 ) 2 ]

TBA-EuMo

5-is similar to that of TBA-SmMo 16 , confirming the robustness of the Sm-POM. The PL spectrum of [Eu(Mo 8 O 26 ) 2 ]

5-in solution shows slight changes compared to that monitored in the solid state. In particular, the weakly intense 5 D 0  7 F 0 transition (576 nm) is distinguishable. In addition, the 5 D 0  7 F 2 / 5 D 0  7 F 1 intensity ratio is increased (0.64 vs 0.38 for TBA-EuMo 16 ). This indicates that the site symmetry of the Eu 3+ ion decreases. [START_REF] Yan | Co-assembly and luminescence tuning of hybrids with task-specified ionic liquid encapsulating and linking lanthanide-polyoxometalates and complexes[END_REF] Nevertheless, as no change is detectable in the Raman spectrum (Figure S5), this symmetry reduction should be limited, and anyway much less pronounced than for EuW 10 which shows a strong inversion of the 5 D 0  7 F 2 / 5 D 0  7 F 1 intensity ratio in water.

8 TPP-EuMo 16 has an intense orange-red solid-state emission at room temperature (Figure S14), with CIE chromaticity coordinates of (0.6281, 0.3666) very close to those of TBA-EuMo 16 . Their PLE and PL spectra (Figure S15) are compara-ble excepted for the 5 D 0  7 F 2 / 5 D 0  7 F 1 intensity ratio which is increased to 0.5 for TPP-EuMo 16 . Upon photoexcitation at 286 nm, the decay time of the 5 D 0  7 F 1 transition is 5.30 ± 0.03 ms (Figure S12), similarly as observed for its TBAcounterpart. This evidences that the substitution of flexible TBA cations by more rigid TPP ones does not significantly impact the high PL performances of [Eu(Mo 8 O 26 ) 2 ]

5-in the solid state. In contrast, the orange emission of TTP-SmMo 16 , which is characterized by CIE chromaticity coordinates of (0.5757, 0.4054), is more intense than that of TBA-SmMo 16 (Figure S14), and the decay time of the 4 G 5/2  5 H 7/2 transition ( exc = 286 nm) reaches 0.66 ± 0.01 ms. This is consistent with the change in the PLE spectrum profile in which the CTS band has the same intensity than the f-f transitions of Sm 3+ (Figure S16), suggesting a better POM-to-Sm 3+ energy transfer.

In summary, the [Ln(Mo 8 O 26 ) 2 ]

5-(Ln = Eu, Sm) complexes are new luminescent Ln-POMs both in solution and in the solid state. The nonsolvated TBA-LnMo 16 compounds have been well structurally characterized. They show a high thermal stability in air and an efficient emission at room temperature. Noticeably, the PL performances of TBA -EuMo 16 5-complexes in acetonitrile. The TPP-derivatives were obtained by a cation metathesis reaction. They are also thermally robust and efficient phosphors. To go further, this work evidences the possibility to design crystallized supramolecular assemblies by combining the luminescent [Ln(Mo 8 O 26 ) 2 ]

5-units with photoactive organic cations, paving the way toward novel multifunctional optical hybrid systems.

ASSOCIATED CONTENT Supporting Information

Experimental section, crystallographic data, IR and Raman spectra, ATG measurements, PXRD patterns, Absorption, PL and PLE spectra, CIE diagrams, luminescence decay curves and extracted lifetimes. This material is available free of charge via the Internet at http://pubs.acs.org.

  New robust luminescent supramolecular assemblies based on [Ln(Mo 8 O 26 ) 2 ] 5-(Ln = Eu and Sm) polyoxometalates Patricia Bolle, Nicolas Albrecht, Thibault Amiaud, Bernard Humbert, Eric Faulques, Rémi Dessapt,* Hélène Serier-Brault* Institut des Matériaux Jean Rouxel (IMN), Université de Nantes, CNRS, 2 rue de la Houssinière, BP 32229, 44322 Nantes cedex 3, France Supporting Information Placeholder ABSTRACT: This work highlights for the first time the photoluminescence (PL) properties of two new [Ln(Mo 8 O 26 ) 2 ] 5-(Ln = Eu, Sm) lanthanide-containing polyoxometalates. Stable crystals of the tetrabutylammonium salts (TBA) 5 [Ln(Mo 8 O 26 ) 2 ] were synthesized, and their structures were confirmed by single-crystal X-ray diffraction. The robustness of the [Ln(Mo 8 O 26 ) 2 ]

Figure 1 .

 1 Figure 1. a) Structure of the [Eu(Mo8O26)2] 5-complex. b) Supramolecular {(TBA)2[Eu(Mo8O26)2]} 3-ribbon. c) Crystal packing in TBA-EuMo16. Green arrows indicate the EuEu distances (blue octahedra = MoO6, gold sphere: oxygen, pink sphere: europium, green sphere: nitrogen, grey sphere: carbon. H-atoms are omitted).

) along with elemental analyses confirm the c h e m i c a l c o m p o s i t i o n

  Figure S5 displays the Raman spectra of TBA-EuMo 16 in acetonitrile solutions at three concentrations i.e., 2 .10 -2 M, 10 -2 M, and 5 .10 -3 M. In the 150-1000 cm -1 range, the Raman peaks characteristic of [Eu(Mo 8 O 26 ) 2 ]

Figure 2 .

 2 Figure 2. a) Excitation spectrum (blue line) monitored at 594 nm and emission spectrum (black line) monitored at 286 nm of TBA-EuMo16. Inset: Photograph of the powder of TBA-EuMo16 upon irradiation at 254 nm. b) Excitation spectrum (blue line) monitored at 600 nm and emission spectrum (black line) monitored at 286 nm of TBA-SmMo16. Inset: Photograph of the powder of TBA-SmMo16 upon irradiation at 254 nm.

  Noticeably, the f-f transitions got a very weak intensity which indicates that the most efficient excitation process corresponds to the CTS. Thus, the -[Mo 8 O 26 ]

7 F 0 7 F 7 F 2 7 F 3

 7077273 electric-dipole transition is absent. The strongest 5 D 0  1 magnetic-dipole transition is split into two Stark components at 590 and 594 nm. The 5 D 0  electric-dipole transition (611-630 nm), which is highly sensitive to the chemical surrounding at the vicinity of Eu 3+ and the 5 D 0  transition (648-661 nm) got weak intensities. In contrast, the 5 D 0  7

5

  This can be explained considering that [Eu(Mo 8 O 26 ) 2 ]

  al. reported tetrabutylammonium (TBA) salts of the [Ln(Mo 8 O 26 ) 2 ]

  are close to those of the EuW 10 reference, owing to structural similarities between [Eu(Mo 8 O 26 ) 2 ] 5-and [Eu(W 5 O 18 ) 2 ] EuMo 16 a promising alternative Ln-POM emitter which is furthermore easily soluble in polar nonaqueous solvents. Both FT-Raman and PL spectroscopies confirmed the integrity of the [Ln(Mo 8 O 26 ) 2 ]

	9-. This makes
	TBA-

G

5/2 -6 H11/2 4 G 5/2 -6 H9/2 4 G 5/2 -6 H7/2 4 G 5/2 -6 H5/2

ACKNOWLEDGMENT

This work was supported by the CNRS, the Université de Nantes, the Ministère de l'Enseignement Supérieur et de la Recherche, and the LUMOMAT project supported by the Région des Pays de la Loire.

AUTHOR INFORMATION

Corresponding Author *E-mail: helene.brault@cnrs-imn.fr (H.B.) *E-mail: remi.dessapt@cnrs-imn.fr (R.D.)

ORCID

Hélène Serier-Brault: 0000-0002-3300-1347 Rémi Dessapt: 0000-0002-2862-7767 Eric Faulques: 0000-0002-7761-8509

NOTES

The authors declare no competing financial interests.

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