André Garenne
email: andre.garenne@u-bordeaux2.fr

Benjamin Pasquereau

Martin Guthrie

Bernard Bioulac

Thomas Boraud

Keywords: Decision making, behavioural task, basal ganglia, information coding

The decision making process is a phenomenon which is hard to track using the standard signal averaging methods such as peri-event time histograms (PETHs). Indeed, even if the sequence of the events is controlled during a behavioural task, the inter-event interval duration remains highly variable. We have applied a temporal normalization method such that PETHs can be mapped across all events of a task trial and compared from neuron to neuron and from session to session. We have also applied Shannon mutual information theory to compare neural activity in recorded striatum and GPi neurons in behaving monkeys during a centre-out motor task and investigated individual neuron coding properties. These methods illustrate information pathways and their relative involvement. We also show that the GPi neurons recorded during the decision phase contained more information about the context and choice combination than striatal neurons.

INTRODUCTION

In a visually-guided motor task, decision-making is a distributed neural process which involves the Basal Ganglia (BG) closely interacting with the frontal and prefrontal cortical areas as well as with the dopaminergic system ( [START_REF] Daw | Dopamine: at the intersection of reward and action[END_REF][START_REF] Kable | The Neurobiology of Decision: Consensus and Controversy[END_REF][START_REF] Opris | Neural circuitry of judgment and decision mechanisms[END_REF][START_REF] Samejima | Multiple representations of belief states and action values in corticobasal ganglia loops[END_REF][START_REF] Schultz | Behavioral theories and the neurophysiology of reward[END_REF]). In a recent electrophysiological study in behaving monkeys, using a multiple choice task, we showed that the encoding of the movement parameter by the neurons of the striatum and the internal Globus Pallidus (GPi) was modulated by the value of the action to be performed ( [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF]). This provides a mechanism by which motor program selection could be performed under dopamine control. However, the selection process, in itself, is inaccessible using classical electrophysiological analysis methods such as post-stimulus time histograms (PSTHs). This is because, even when a cue is presented at a known time, the actual moment of decision making cannot be observed and so its temporal relationship to the cue and other events cannot be known. To access the neural mechanisms underlying this process, we need to closely link the electrophysiological activity to the behavioural events during the whole task. To do so, we have computed for every neuron a multiple event PETH. Moreover, experimental protocols for decision making assessments (including our own studies) assign a randomly variable duration between task events. This means that the length of time between these events varies from one event to another and from trial to trial for the same event. This, along with the fact that cognitive reaction time varies from trial to trial for each animal, prevents the direct comparison of the time course of the PETHs. To solve this conundrum, we propose a method that allows us to normalize time durations in each trial (see methods). We applied this method to data previously recorded in the main input and output stages of the BG (respectively, striatum and GPi) of 2 monkeys (M1 and M2) during a reward probability based free choice motor task that we designed (Figure 1, see [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF] for details). This task encompassed 7 successive events. This normalization method is applied to the whole trial duration because BG activity is notoriously variable and may have dynamic encoding capacities ( [START_REF] Arkadir | Independent coding of movement direction and reward prediction by single pallidal neurons[END_REF]). In our experiments monkeys were over-trained and maximized their payoff by choosing the target with the higher reward value (for details see [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF]). This gives 2 possible encoding strategies for the BG. First, it may just encode the chosen target. Secondly, its activity may be related to the sensory context of the trial ( [START_REF] Mink | Basal ganglia motor control. II. Late pallidal timing relative to movement onset and inconsistent pallidal coding of movement parameters[END_REF]). Therefore we then specifically focused our analysis on the possible correlation between the neuronal activity during the crucial period preceding movement and the context of the task or the ongoing decision: the decision phase (DP). Using these methods, we addressed the question of what the system encodes.

MATERIALS AND METHODS

The reader is invited to refer to the first paper dealing with these data ( [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF]) for an exhaustive description of materials and methods. Here we provide a summary including only the details necessary to explain the additional analyses and results.

Animal training and surgery

In the task (Figure 1) monkeys were trained to move a custom-made manipulandum in a horizontal plane with their right hand. In each trial of a session, 2 different cue targets (randomly chosen from a set of 4) were displayed simultaneously on the screen. Each cue appeared randomly in one of 4 possible directions and was associated with a specific probability of a reward being delivered at the end of a successful trial (P(R) = 0, 0.33, 0.67 and 1). The reward probability remained the same throughout a session. In order to induce a situation in which there was always a "better" choice, a single trial could not include 2 identical cues or 2 targets in the same location. After a random period (1-1.5 sec), the "go" signal was given and the monkey had to initiate a movement towards one of the 2 targets. Once he reached this position, he had to hold the cursor on the target for another random period (0.5-1.0 sec) after which the animal had to move the cursor back to the initial, central position. The reward was then delivered (fruit juice) according to the probability associated with the selected target. For each successful trial, if the monkey chose the target associated with the highest probability of receiving a reward, her choice was defined as optimal. If not, she could still receive her reward with a probability equal to that for the chosen target. For purposes of analysis of the context dependent choice, we consider that the context in which the animal is making the decision is the combination of 2 targets that are visible during a trial. Thus, with 2 targets selected from 4, there are 6 possible combinations and therefore 6 distinct contexts within which the animal makes a decision on which target to choose.

Recording and data acquisition

Neuronal recording was performed in the dorsolateral striatum and the GPi using an implanted recording chamber ( [START_REF] Bezard | Pallidal border cells : an anatomical and electrophysiological study in the MPTP-treated monkey[END_REF][START_REF] Boraud | Dopamine agonist-induced dyskinesias are correlated to both firing pattern and frequency alteration of pallidal neurons in the MPTP-treated monkey[END_REF]). Data acquisition, spike sorting and storage have been previously described ( [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF]). The behavioural events were stored simultaneously with the electrophysiological recordings (Figure 1): trial begin (TB), cue presentation (CP), go signal (GS), on target period (OT), back home period (BH), reward/no reward event (RE/NRE) and finally trial end (TE).

Data analysis

The analyses were performed with custom-made Matlab scripts (MathWorks, Natick, MA), C# programs (Microsoft) and NeuroExplorer tools and scripts (Nex Technologies, Littleton, MA).

Global PETH extraction and analysis

PETHs extraction and normalization

The analysis of electrophysiological data coupled with behavioural events often relies on PETHs of single events occurring during the task. Their computation by itself, does not provide a framework for statistical inference ( [START_REF] Czanner | Analysis of between-trial and within-trial neural spiking dynamics[END_REF]), but despite this intrinsic limitation it remains a widely used reference tool that often provides meaningful insights. To have an overall view of the neuronal dynamics associated with the choice task and to compare both striatal and pallidal activity profiles, we investigate the temporal outline of PETHs across all the steps of the task. Therefore, to focus on the particular involvement of striatum and GPi in these dynamics and their relationship to the experimental conditions, we have implemented an algorithm that can identify behavioural event sequences of interest and extract the spike trains related to these events. Dedicated C# software scrutinizes the spike trains and computes the PETH for every recorded neuron. In a first step, it extracts all the recorded sequences where the monkey completed every event through the course of the trial (the event sequence: TB-CP-GS-OT-BH-RW-ET) and discards sequences where any event was not completed (e.g. where the monkey failed to return the cursor to home). In a second step, all trials in which no reward was gained were discarded. This is because the firing profile in cases where reward is obtained and those where no reward is obtained are necessarily different. Therefore, in the presented results only successfully completed trials where a reward was obtained are shown so that the same behavioural profile is always under consideration. The time normalization of the PETHs is computed as follows: in every trial and for every neuron, the first inter-event interval (IEI) is split into the same number of time bins. The duration of a bin in one trial is thus not equal to that in another trial.

For instance, the first IEI is always split into 100 bins.

As the duration of this event can vary from 1s to 1.5s, the length of a bin can vary from 10ms to 15ms. Based on this bin size and on the following IEI averaged durations, an average number of bins is allocated for each IEI. Since between different neurons, the IEI average durations are similar (because most of the random durations are generated by the software itself), this time normalization technique allows the comparison of their PETHs. At the same time, amplitude normalization is applied on the PETHs based on the maximum number of spikes observed at any point in time over the whole time course of a trial. Using this method, we have performed new analyses of the data of a previous publication by our team. In this analysis we assume that similarity of form of the PETH over the course of the events of a trial implies similarity of function of the neuron in the decision making process.

PETH analysis

We compare PETH distributions between striatum and GPi. Our main goal is here to find global salient features in the neuronal activity of the 2 structures from a temporal point of view. To achieve this, the correlation coefficient matrixes are computed between every neuron PETH, separately for each monkey. These analyses are performed separately for the 2 monkeys and for striatum and GPi. All statistical tests used here are student-t tests, p<1%.

Extraction of "Coding neurons"

The monkey's decision occurs after the CP (cue presentation) and before the movement initiation triggered by the GS (go signal). Whilst this period of time, from CP until GS, includes the decision process phase itself, it may also include an amount of time during which the monkey just waits for the GS and it is not easy to differentiate between the two ( [START_REF] Leblois | Late emergence of synchronized oscillatory activity in the pallidum during progressive parkinsonism[END_REF]). We compute this Decision Phase Averaged Firing Rates (DPAFR) for each neuron and for each different context presented to or choice made by the monkey. We first extract the neurons for which significant variations in firing rate are related to any of the 6 different context values or to any of the 3 choice reward probabilities by applying a one-way ANOVA. When the ANOVA is positive, we apply post-hoc methods based on the Tukey's least significant difference procedure. These analyses are performed with the Matlab Statistical toolbox and separately both on the 2 monkeys and on striatum and GPi. We thus obtain tuning curves with preferential choice and/or coding context values for each of these "coding" neurons that are later applied to basic modeling studies.

Signal carried information analysis

We compute mutual information between the firing rates and the context value, for coding neurons. The mutual information, I, between 2 discrete random variables X and Y is given by: where p(x,y) is the joint probability distribution function of X and Y, and p(x) and p(y) are the marginal probability distribution functions of X and Y respectively. The results are used to investigate the respective involvements of the GPi and of the striatum in the processing of information of context encoding in BG.

Model prediction

For every coding neuron in both structures, the tuning curve exhibits a preferential context/choice value encoding (e.g. one neuron may have its highest DPAFR when the target with 0.66 and the target with 0.33 probability of reward are presented together). For each previously extracted coding neuron, our predictive model thus associates the 6 different reference DPAFRs of the tuning curve with each of the 6 different context values (and respectively the 3 DPAFRs associated with each of the 3 choice values). The model is then used this way: DPAFRs are computed for each trial of a given coding neuron. For every trial, the experimental DPAFR is applied as an input to the tuning curve (core of the model) which returns the most likely context (i.e. that for which reference DPAFR is the closest to the experimental DPAFR). When the theoretical values are the same as the actual, the trial model prediction is considered as successful. Success rates are then computed for context and choice encoding in both monkeys and in both striatum and GPi. The prediction quality of the model is then compared to random choices based on context and choice respective chance based rates (16.67% and 33.33% to obtain the actual value with a random draw). Using a Kolmogorov-Smirnov test, we first compute the significance of the model retrieval rates compared to the chance based rates. A Wilcoxon rank signed test is then used to compare the power of the model concerning context and choice prediction in order to conclude which one is most efficiently encoded in the recorded structures. Real population coding investigations are not achievable since our data only allow us, at best, 2 or 3 different neuronal spike trains sources during the same session. However, through several examples, we emphasize here some trends of multiple neurons encoding and of their numerical effect on context or choice prediction rates.

RESULTS

PETHs extraction

The

The population activity synchronization differs between striatal and pallidal neurons.

The PETHs correlation coefficients matrices are computed separately for both monkeys and for striatal and GPi neurons. The 3 average correlation coefficient (ACC) combinations (GPi-striatum, GPi-GPi and striatum-striatum) are computed and compared. As predicted after a visual control of Figure 2, clear differences are revealed between the 2 regions regarding the neuronal dynamics, as shown in Figure 3.A and Figure 3.C. The PETHs correlation coefficient values appear higher among GPi neurons than striatal neurons in both monkeys. This demonstrates that there is less dynamic variability between GPi neurons and this is confirmed by the estimate of their ACC values according to the structure. As shown in Figure 3.B and Figure 3.D, the ACC values differ significantly between the 2 structures. This emphasizes a higher temporal synchronization of GPi neuronal spike trains compared to striatum. This result is the same in both monkeys. Moreover, the lowest absolute value of correlation coefficient occurs in both monkeys when computing the ACC value between GPi and striatum which is another argument in favour of a possible functional dissociation between the 2 structures.

Data modeling by coding neurons

Only those neurons that showed an average firing rate that was dependent on the context or choice during the decision phase were used for analysis of the coding. For M1, 41.51% of the striatum and 21.57% of the GPi neurons and for M2 29.82% and 10.71% displayed such a property. Mutual information between context/choice values and NFRs during the decision phase was computed. The amount of information carried by striatal neurons is less than that carried by GPi neurons during the DP (Figure 4.A and Figure 4.C). The firing rates of GPi neurons yielded more information on both the context and the choice values than the firing rates of striatal neurons in both monkeys. The GPi neurons thus appear as more reliable encoders. This implies that the context and/or the choice values are refined between the striatal and the pallidal processing stages and therefore suggests an information convergence mechanism between the striatum and the GPi. These results are subsequently confirmed and refined by the modeling studies. Every context or choice dependant tuning curve of coding neurons is extracted and applied to its originating spike train from which the tuning curve was constructed. This allows us to estimate the efficiency of the model in reconstructing the original choice and context values. reconstruct the original data and on its retrieval capability. This allows us to compare the predictive power of GPi and striatal neurons. Considering, firstly, the context or choice prediction rates, we can deduce 2 prominent features. The first is a significant difference between striatal and GPi neuron's success rates. The second is a significantly higher retrieval rate for pallidal neurons compared to striatal neurons. This latter result corroborates the previous mutual information outcomes and confirms a greater involvement of the GPi compared to striatum in both context value and choice encoding and thus an information convergence process. The third and last result is obtained by comparing the averaged level of context and choice encoding success rates taking into account their proportion related to chance. From this, we can compare their unbiased respective retrieval success rates. As shown in Figure 4.B and Figure 4.D, the success rate profiles of context and choice encoding are similar between the 2 monkeys. In a first step we compare the actual success rates of the model to the success rates due to chance. For this, the results give a binomial distribution with a success base probability value of 16.67% for context and 33.33% for choice. Kolmogorov-Smirnov tests applied for both monkeys for both striatum and GPi vs. chance give p-values of p < 1% for both context and choice. These preliminary results confirm that the model predicts both context and choice at a level far greater than chance. In the second step we subtract the success base chance rate from the actual model results to remove bias and compare the predictive power of the model in context and choice encoding ( [START_REF] Bernard | Mesures statistiques en épidémiologie[END_REF]). The Wilcoxon signed rank test is then applied to the unbiased data using an alternative hypothesis of "less" for the choice prediction. For both monkeys and both anatomical structures p-values < 1% are obtained. This suggests that, during the decision phase, the average value of the firing rates of the GPi and striatal neurons preferentially encodes the context rather the choice value.

DISCUSSION

This study presents a novel attempt to shed light on the correlation between BG neuron spike train dynamics and behavioural decision making tasks. It provides evidence that encoding neurons show 2 remarkable properties: i) the firing activity of GPi neurons during the decision phase carries more information on the context and on the choice values than the striatal neurons and ii) both structures preferentially encode the context rather than the choice.

Our study reveals a higher level of synchronization inside the GPi than in the striatum. This feature is evidenced both by the ACC analysis (Figure 3) and the computation of entropy (results not shown here). It confirms our previous work ( [START_REF] Pasquereau | Shaping of motor responses by incentive values through the basal ganglia[END_REF]) where we showed that during the executive part of a choice task, the GPi activity is strongly related to the action performed (encoding mainly movement parameters and action value), while the striatum remains more versatile, encoding different parameters (chosen target value, non chosen target value, motor parameters, action value, etc) at more closely comparable levels. This study confirms these observations and shows that this focus on the action to perform in the output structure of the BG is associated with a high correlation level. These data may seem at variance with another study showing decorrelation between GP neurons in a discrimination task ( [START_REF] Joshua | Encoding of probabilistic rewarding and aversive events by pallidal and nigral neurons[END_REF]). However, the Joshua et al. study used a noninstrumental task (the animal has no action to perform in response to the cues), while, in our study, the choice between the 2 options and its expression by a consequent action is an essential aspect of the task. When we consider these 2 studies, it thus reinforces the hypothesis that the very significant and transient synchronized response in the GPi neural population reflects the decision making and action selection processes occurring in the cortico-basal ganglia loop.

When we focused our analysis on the decision period, we used 2 methods to assess the relationship between the neural activity of the BG and the choices performed by the animals (Figure 4). Both reveal a better correlation for the encoding of the context than for the encoding of the choice and both show that the GPi is a much better predictor than the striatum of both parameters. These data imply that during the critical decision phase, when the animal decides which action to perform, the BG are deeply involved in the computation process which leads to the decision. The fact that the input stage (the striatum) is less correlated than the output stage (the GPi) to the actual behavioural parameters is a further confirmation of the importance of the BG in the process. 2 hypotheses can explain why the correlation is higher for the context than for the choice: i) the BG encoded preferentially the context or ii) the BG take into account the context in order to perform a choice. The latter hypothesis has already been proposed by other teams ( [START_REF] Morris | Midbrain dopamine neurons encode decisions for future action[END_REF][START_REF] Niv | Choice values[END_REF]) and is supported by the fact that the cortico-basal ganglia loop could be considered as a SARSA learning system and encodes the combination of choice made and context within which the choice was made. Unfortunately, because in our task the monkeys optimize their behaviour (thus maximizing their gains), it is impossible to rule out either of these hypotheses. This work is a first attempt to analyze comprehensively during the full duration of the trial the process of neural computation occurring in the BG during a behavioural task. The high variability of BG neural population firing rates, especially in the output stage makes this solution better than the classical PSTH which reduces the richness of the neural responses. The approach we have adopted allowed us to visualize and analyze the decision period and allowed us to demonstrate the crucial role played by this structure in the decision making process.

Figure 1 :

 1 Figure 1: Behavioral paradigm. The reward probability-based freechoice task. 2 different targets associated with reward probabilities (here P(R)=0.33 and P(R)=0.67) are displayed simultaneously during each trial (Cue), in 4 possible positions in random order (6 target combinations) and in random locations (4x3 possibilities).

  software successfully extracts and normalizes both in time and amplitude the global PETHs from all recorded neurons and according to the previously defined sequence of events. The present study is based on 111 striatal cells (53 in M1 and 58 in M2) and 107 pallidal cells (51 in M1 and 56 in M2). Examples of normalized PETH distributions among striatal and pallidal neurons in M1 are given respectively in Figure 2.A and Figure 2.B. They clearly emphasize region dependant disparities among neurons and regarding the activity profile throughout the task. We found the same region dependent disparities in the recordings of M2 (not shown).

Figure 2 :

 2 Figure 2: plot of 53 recorded neuron PETHs from the striatum (A) and of 51 neurons from the GPi (B) of M1.

Figure 3 :

 3 Figure 3: Cross-correlation matrix of all the neurons PETHs for M1 (A) and M2 (C). Boxplot of ACC values for GPi vs. GPi (CC1), striatum vs. striatum (CC2) and GPi vs. striatum (CC3) of the neurons PETHs for M1 (B) and M2 (D) (Student t-test, p<1%).

Figure 4 .

 4 B and Figure 4.D summarize these computations. This simple empirical method provides information on both the ability of the model to

Figure 4 :

 4 Figure 4: Mutual information between decision phase average firing rate and context and choice values for M1 (A) and M2 (C). Prediction model success rates for M1 (B) and M2 (D). The Random series represents the success base chance to predict the correct values (respectively 1/6 for context and 1/3 for choice).

INFORMATION ENCODING AND PATHWAYS IN BASAL GANGLIA

NEURONS.


Bruno Delprat
email: brunodelprat@club-internet.fr

Mohamed Hallab
email: mohamed.hallab@yahoo.fr

Martine Cadot
email: martine.cadot@loria.fr

Alain Lelu
email: alain.lelu@univ-fcomte.fr

Processing a Mayan Corpus for Enhancing our Knowledge of Ancient Scripts

The ancient Maya writing comprises more than 500 signs, either syllabic or semantic, and is largely deciphered, with a variable degree of reliability. We applied to the Dresden Codex, one of the only three manuscripts that reached us, encoded for L A T E X with the mayaT E X package, our graded representation method of hybrid non-supervised learning, intermediate between clustering and oblique factor analysis, and following Hellinger metrics, in order to obtain a nuanced image of themes dealt with: the statistical entities are the 214 codex segments, and their attributes are the 1687 extracted bigrams of signs. For comparison, we introduced in this approach an exogenous element, i.e. the splitting of the composed signs into their elements, for a finer elicitation of the contents. The results are visualized as a set of "thematic concordances": for each homogeneous semantic context, the most salient bigrams or sequences of bigrams are displayed in their textual environment, which sheds a new light on the meaning of some little understood glyphs, placing them in clearly understandable contexts.

I. INTRODUCTION AND PROBLEMATICS

The logo-syllabic writing of the ancient Mayas, in use during more than 13 centuries, reached us through rich inscriptions on monuments, ceramics and three divinatory almanacs, which constitute nevertheless a small volume of available texts: three manuscripts and about a thousand short inscriptions.

The objective of the work here presented is to retrieve the main semantic contexts of glyphs usage, in the spirit of [START_REF] Rosh | Cognitive representations of semantic categories[END_REF] approach to semantic categories, in order to bring together in a common context deciphered glyphs, and those which are less or not at all understood. On the long run, it could result in providing the mayanist scientific community with such a contextualization for the whole available Maya corpus.

We chose for this first computer encoded corpus a representation method characterized as follows:

1) unsupervised, so that from co-occurrences of glyphs, or other text attributes, arise interpretable contexts comparable to what is already known, 2) fuzzy: to every statistical unit, elementary text or attribute, is allocated a centrality value which strength varies with the various uncovered contexts. Accordingly, elements with a weak representativeness in the analysis will show low values in all contexts; polysemous or syntactic elements will be central in several contexts, i.e. show a strong value in several clusters; elements with a univocal signification will be central in a single cluster only 1 , 3) compatible with the relative scarcity of available sources, by contrast with the statistical approach to language models that require to collate millions of occurrences [START_REF] Brun | Experiment analysis in newspaper topic detection[END_REF].

II. PRINCIPLES OF MAYA WRITING AND ITS ENCODING FOR L

A T E X The elementary sign of writing is the glyph. One or more glyphs are assembled together to harmoniously fill the preset rectangular space of a cartouche. Maya manuscripts texts are organized in blocks of 2 to 16 cartouches which constitute as many sentences, often followed by associated numbers, dates and possibly a picture. Depending on the number of cartouche slots available on the almanac page for writing a short or long sentence, the scribe would squeeze in or spread out writing signs among the cartouches to avoid empty boxes and obtain a nice looking page layout.

A. General principles of Maya writing

Through the analysis of the Maya codices of Dresden, Madrid and Paris, we determined that a complete glyphic cartouche is made of 1 to 5 basic signs or glyphs, from a catalogue of 509 glyphs. Affixes, like 031 ni, present rotation patterns and symmetries, following a determined rule, around the central elements such as 204 Ì which orientation is fixed. Affixes are generally syllabic value signs which can combine together or with a central element to write a Maya word. Central elements are generally of logographic nature, corresponding to a morpheme or a word, and read globally like 204 Ì KIN sun, day. The general orientation rule of the affixes is the following:

(063) te ? ?

? ?

For example : ?Ņ Ɠ , ? ò ? u ?

A complete glyphic cartouche often corresponds to a lexical entry with preceding and following grammatical affixes as in 204.031 Ì KIN-ni sun, day, but it can also in some cases correspond to two words if they are short, or more rarely otherwise to a part of an expression spelt over two cartouches.

B. Maya glyphs computer input and composition with mayaT E X

In the early 1960s' Soviet cryptologists and historians [START_REF] Évréïnov | Primenenie elektronikh vychislitel'nykh mashin v issledovanii pis'mennosti drevhikh mayia [Utilisation des machines calculer électroniques pour les recherches sur l'écriture des anciens mayas[END_REF] undertook the first computer encoding of the cursive maya writing in a catalogue of about 500 glyph forms, then coded on magnetic tape the Dresden and Madrid codex to process the texts with the computer possibilities of that time, a pioneering work almost completely forgotten since.

A prerequisite to the computer encoding of Maya texts is the structural analysis of the written form of the codices, which includes the formulation of basic hieroglyphic signs composition rules within the Maya cartouche and the definition of a graphic grammar, work done as part of an ongoing doctoral dissertation [START_REF] Delprat | Le codex de dresde: Paléographie et traduction comparée d'un almanach maya du 15 eme siècle[END_REF].

MayaT E X [START_REF] Delprat | maya -un sistema de composición tipográfica de textos jeroglíficos mayas para la computadora[END_REF], an original computer tool for the input and edition of Maya hieroglyphic texts developed under T E X, is used for the composition of the palaeography and the dictionary included in the dissertation. The two main glyph composition operators within a Maya cartouche are the point "." which associates two elements 117 u and 260 Ą by left-right juxtaposing 117.260 uĄ , and the slash "/" which places an element 400 Ɛ above another one 010 to yield 400 / 010.030 Ɛ . Operators ".

" or "/" are also active on a subset of glyphs in brackets (154.123) { , to yield (154.123)/177 ± { .

Ligatures: One or several affixes or central elements can be melted inside a geometric central element or, more frequently, inside a head variant instead of being simply attached to it, forming a ligature as a single bound form. Ligature glyphs appear in the catalogue as graphic elements with specific codes 373 ŵ Cacau D7c (2), which in fact decomposes into simpler glyphs: 369<023/023>. The operator < > indicates that both affixes 023 are placed in the centre of 369 ű . Within Maya texts, both forms: melted as a ligature (described by one code), and separately drawn (described by 2 -3 codes) are equivalent and constitute graphic variants. Our catalogue includes 108 ligature glyphs.

III. THE DRESDEN CODEX AND ITS DECIPHERMENT Figure 1. Dresden codex Segment 30b

A divinatory almanac: The Dresden codex, one of the three only handwritten Mayan texts which reached us and dating probably from the 15th century, is constituted of all 76 almanacs of 5 main types: divinatory almanacs of Tzolkin calendar of 260 days dedicated to various divinities, prophecies of Haab solar year of 360 days plus 5 extra leap days, and of Katuns or cycles of 52 years, almanacs of four cardinal directions dedicated in Chac, the God of the water, astronomic tables such as the stages of Venus, solar eclipses and lunar eclipses, and almanacs of the formalities of the New Year and of the flood associated with Katun cycle of 52 years. These texts are in general independent one another and not the successive chapters of a Western book to be read from the beginning to the end.

Figure 1 reproduces the middle segment, numbered 30b, of folio 30 with the corresponding hieroglyphical palaeography of the 2nd text block from the left encoded under mayaT E X. This almanac is part of a series dedicated to the tasks performed by Chac, the God of rain and water, who appears in the form of the avatars of the four directions. Corresponding offerings are a dish of meat and a particular colour tribute for each of the four directions: The text corpus: The 74 codex folios, numbered by [START_REF] Förstemann | Die Maya-Handschrift der königlichen Bibliothek zu Dresden[END_REF] and encoded following the catalogue of [START_REF] Évréïnov | Primenenie elektronikh vychislitel'nykh mashin v issledovanii pis'mennosti drevhikh mayia [Utilisation des machines calculer électroniques pour les recherches sur l'écriture des anciens mayas[END_REF] with some complements for mayaT E X, do not read in a linear way the one after another. Indeed, every divinatory almanac or text with astronomic table of the codex is painted across several folios, for example the upper segments of folios 4a, 5a, 6a and 10a. The text statistical units considered in this research are the 214 folio segments as defined by the Maya scribes, generally separated by a red line, which usually correspond to upper, middle or lower part of folios.

Ɛ Ì ° uĄ o ȃ Ƨ
Each folio segment includes 1 to 8 blocks of hieroglyphic cartouches, one block holding for one sentence. The distribution of the number of sentences per folio segment is concentrated: 77% of the segments include 2 to 4 sentences (see Figure 2).

From a statistical point of view, the Dresden codex corpus is composed of 9938 glyphs including dates and numbers, or 7549 proper text glyphs, composed of 409 individual writing signs, among which 345 textual elementary or ligature glyphs. Individual glyphs occur in the codex with 1 to 252 repetitions 2 . Unsurprisingly, the distribution of the glyphs follows a Zipfian allure (see Figure 3), linear in log-log coordinates and typical of a power law, common to all corpuses from any language origin, confirming that Maya glyphs write human language. The size of the text segments, measured by the glyph number, follows a distribution law 2 In fact, the most represented sign with 411 repetitions is 001 replacing an erased text glyph. Syllabogram affixes 111 o li and 026 u-(his, her, 3rd person relative pronoun) are the most frequent textual glyphs both with 345 occurrences. with a binomial allure (see Figure 4), as text segments in many other corpuses do. Each sentence includes 1 to 26 cartouches, including numbers and dates. The above-mentioned aesthetic requirements account for the fact that more than one sentence upon three consists of exactly 6 boxes. It follows also that about one segment upon four is composed of three sentences made of 6 boxes. The corresponding distributions are thus very asymmetric, with a strong modal value, respectively 6 boxes per sentence and 18 boxes per segment. The decipherment: It benefits from favourable factors: the Mayan languages are still spoken at present, and we have at our disposal the prophecies of the Chilam Balams [START_REF] Vásquez | El libro de los libros de Chilam Balam[END_REF], which are partly the Yucatec transcription in Latin alphabet of divinatory texts similar to the ones found in the three remaining hieroglyphical divinatory codices. The meaning of the logo-syllabic signs, i.e. glyphs, is established with certainty for more than a fifth, and with reasonable credibility for more than a half. . In spite of this constituent commutability, one may notice a large majority of frozen textual cartouche arrangements: as the whole corpus comprises 3034 cartouches of text with 1258 unique occurrences, 1197 of them are composed of glyphs that strictly show no variation of their graphical layout, which amounts to 79% of the occurrences. In the 61 remaining occurrences, the glyphs may be turned around or permuted. It is noticeable that no more than 19 of the latter give rise to variants, in the coding of which the ordering of the basic (i.e. non-positional) codes

IV. THE PROCESSING CHAIN

The corpus encoded under mayaT E X was first preprocessed to extract n-grams of individual glyphs. Then, a further described clustering algorithm, programmed with Scilab, provides for each cluster the ordered and valued lists of n-grams and documents (i.e. folio segments, see below) that characterize the cluster. In a post-processing stage, these lists are improved appending their context cartouches, and visualized using mayaT E X to enable their linguistic interpretation.

One may oppose that the glyph-codes ordering induced by the chosen coding scheme is fairly conventional, and that it should be better to use, instead of bigrams, unordered glyph "2-itemsets" occurring within a cartouche, whatever their graphical placing: the dominant frozen configuration reported at the end of section 3 shows that such a coding scheme would be needlessly redundant, compared to a simple bigram coding rule. Of course this freezing may be due to the sole writing habit of one putative scrivener: the coding of the entire Maya known corpus (the three codices and the diverse other written material) may necessitate such an extra coding convention.

A. Pre-processing

Choice for the split into text units: How to split the corpus into text statistical units -the comparison of which is the rationale for the analysis -directly impacts the granularity of the analysis: too fine a split, for example at cartouche or glyph level, would favour syntactic elements, not our present objective; a rougher split would privilege semantic elements, but the risk then is ending up with too few elements to obtain a clustering at the wished fineness level. The in-between solution adopted here is to consider folio segments as defined by the Maya scribes, knowing that the texts in these segments can be spread out on several folios. The number of page segments is a priori compatible with a granularity of analysis needed for around ten semantic clusters, allowing to go beyond obvious and known text divisions (stages of Venus, prediction of eclipses, etc.). A finer division, at the level of the Maya sentence was also tested, to validate our splitting up choice, and to extend the analysis onto the syntactic plan.

Excerpt from text segment 5b:

ł oĒ Έ ̦ ⇒ Maya sentence oĒ ⇒ cartouche o ⇒ glyph; Ē ⇒ glyph

̦

⇒ cartouche Why n-grams ? Choice of n: For the experiments presented here we decided to characterise each portion of text by its vector of glyph bigram frequencies, as they appear from mayaT E X coding: observed combinations of these bigrams, considerably lesser than 500 2 , can be easily handled with current computer technology without needing to recur to a H-coding compression of the number of codes, as we did in the context of other applications in the past [START_REF] Lelu | Recherche d'information et cartographie dans des corpus textuels partir des fréquences de n-grammes[END_REF]; our present choice is not to have bigrams crossing cartouche borders, as cartouches correspond most frequently to distinct phrases. The use of bigrams constitutes a flexible and minimal way of reflecting text sequentiality. Maya bigrams correspond most often to a part of the 3 to 5 signs cartouche, and therefore to words or phrases which are displayed after each bigram in the tables.

Our software for presenting the results post-processes the (coded) outputs of the clustering stage, and was adapted to the specificities of the Maya writing. One of the difficulties we had to solve was the following: glyph codes are surrounded by position codes (above/below, sign symmetry or rotation, ...) that are easy to filter to obtain glyph bigrams free from this information. The other way round, it is necessary to restore these elements to display all the salient bigrams in a cluster in their original graphic context: we chose to provide the mayanist user, for each important bigram in a cluster, with all different cartouches to which it participates, establishing a kind of a concordance list at the level of each cluster.

Extraction of n-grams: Original texts are transformed by reduction of position characters /:< and filtering orientation attributes () * ?-! + @| >. A window of length 7 (2 Maya glyphs separated by a point) moves along the text, 4 characters at the same time. A blank space stops current scrolling by the N=2 glyphs window, then re-initializes it.

B. The unsupervised learning process

Distributional distance and cosine: A series of ancient works [START_REF] Matusita | Decision rules based on distance for problems of fit, two samples and estimation[END_REF], [START_REF] Escofier | Analyse factorielle et distances répondant au principe d'équivalence distributionnelle[END_REF], [START_REF] Domengès | Analyse factorielle sphérique: une exploration[END_REF], [START_REF] Rao | A review of canonical coordinates and an alternative to correspondence analysis using Hellinger distance[END_REF] focused on what some authors coin as distributional distance, and others Hellinger distance: it deals with the usual Euclidean distance (equally weighted dimensions), between two points t 1 and t 2 , the coordinates of which are given by the vectors z t 1 and z t 2 , at the surface of the unit hypersphere in the space of the I descriptors. These points depict text segments, defined by the following transformation of the original frequency count data:

z t1 : x it 1 x .t 1 ; z t2 : x it 2 x .t 2 (1)
where x it is the frequency count of descriptor i in segment t, and x .t is the total number of descriptors in segment t.

The distributional distance Dd(t 1 ,t 2 ) between the text segments t 1 and t 2 yields:

Dd(t 1 ,t 2 ) = ||z t1 -z t2 || (2)
where ||x|| stands for the Euclidean norm of vector x.

This distance is the length of the chord associated with the (z t 1 , z t 2 ) angle -it equals 2 when the vectors are opposite, √ 2 when they are orthogonal. This distance may seem trivial and somehow arbitrary, as one may question why such an unusual normalization instead of the usual colinear one

x it ||x t || , but its properties are interesting: 1) Contrary to the χ 2 distance underlying Correspondence Analysis [START_REF] Benzécri | L'analyse des correspondances[END_REF], it can take into account vectors with negative components, a useful property for "symmetric" codings such as Yes / No / Dont know, or oriented flow matrices -for economics, physics, ... 2) This distance is closely connected to Renyi's order 1 2 information gain [START_REF] Renyi | Calcul des probabilités[END_REF] provided by a distribution x q when the distribution x p is known:

I (1/2) (x q /x p ) = -2 log 2 (cos(z p , z q )) = -2 log 2 1 - Dd 2 2 (3)
3) It is specially suited to "directional data" [START_REF] Banerjee | Clustering on the unit hypersphere using Von Mises-Fisher distributions[END_REF] vectors such as encountered in textual data, the angle of which are relevant, not their lengths, 4) When the z t vectors are sparse, as is the case for text data, computation time is strongly reduced, 5) Last but not least, [START_REF] Escofier | Analyse factorielle et distances répondant au principe d'équivalence distributionnelle[END_REF], [START_REF] Domengès | Analyse factorielle sphérique: une exploration[END_REF] have shown that it benefited from the same "distributional equivalence" property as the χ 2 distance used in Correspondence Analysis: when two descriptors with the same relative profile are merged, the distances between text segments are unaltered. In other words, this property ensures the stability of the distance system when elements with similar distributions are merged or split, whatever column-wise or row-wise. Our unsupervised clustering method: The principles at work in the axial KMeans clustering method [START_REF] Lelu | Clusters and factors: Neural algorithms for a novel representation of huge and highly multidimensional data sets[END_REF] are:

1) turning the documents raw data cloud, i.e. data cloud of the text segments, into a normalized data cloud at the surface of the unit hypersphere by means of the (non-colinear) mapping:

x i j → x i j x i. (4)
where x i. is the sum of the ith document-vector x i , 2) splitting this cloud into K sub-clouds, each one provided with an axoïd issued from the centre of the hypersphere. Each point belongs then to the cluster of its maximum projection on all axoïds. The axoïd of each sub-cloud is defined as the first component extracted by Spherical Factor Analysis (SFA) [START_REF] Domengès | Analyse factorielle sphérique: une exploration[END_REF] ] ("difference to the null data table" option): in matrix notation, if X is the (document × attribute) data table, summing to x i. and x . j row-wise and column wise respectively, if D

-1 2 r is the diagonal matrix of x -1 2 i. (respectively D -1 2 c with x -1 2 . j
), the singular value decomposition (SVD) of:

X 1 2 = x 1 2 i j writes : X 1 2 = UDV ′ (5)
where the prime sign indicates the transposition of a matrix, and where the orthonormality conditions:

U ′ U = V ′ V = I hold. (6)
The SFA factors write:

F = D -1 2 r UD (7)
G = D -1 2 c VD (8)
The reconstitution of the data writes:

X 1 2 = D 1 2 r FD -1 G ′ D 1 2 c (9)
Note that this process is formally related to correspondence analysis (CA), where SVD applies to the transformed matrix:

Q = D -1 2 r XD -1 2 c ( 10
)
leading to: [START_REF] Escofier | Analyse factorielle et distances répondant au principe d'équivalence distributionnelle[END_REF] and where the CA factors write:

Q = U ca D ca V ′ ca
F ca = x 1 2 .. D -1 2 r U ca D ca ( 12
)
G ca = x 1 2 .. D -1 2 c V ca D ca (13)
Eventually, the reconstitution writes:

X = 1 x .. D r F ca D -1 ca G ′ ca D c ( 14
)
Geometrically speaking, CA maps the raw data cloud onto the surface of a "stretched simplex" [START_REF] Greenacre | The geometric interpretation of correspondence analysis[END_REF] whose barycentre is pointed out by the first factor, a trivial vector of ones (the corresponding first eigenvalue is equal to one).

This contrasts with the SFA, where the document factors, i.e. projections of the documents onto the first axis, define the centrality indices of these documents 3 , and the squared first eigenvalue λ 2 1 defines the portion of the data table sum x .. accounted for by the first-order reconstitution of:

X ≃ x i j = 1 λ 1 F 2 1 (i)G 2 1 ( j)x i. x . j ( 15
)
where F 1 (i) stands for the i-th component of the first rowfactor, and symmetrically for G 1 ( j).

In our specific clustering application, the sum over all clusters of their squared first eigenvalue accounts for 25.21% of the data.

In the perspective of our present analysis, an important property is that of duality: to the principal axis of the document data cloud, expressed by a vector with one coordinate per attribute, corresponds the formally symmetric principal axis of the attribute data cloud, expressed by a vector with one coordinate per document ("transition formula"):

F 1 = 1 λ 1 D -1 2 r X 1 2 D 1 2 c G 1 (16)
This approach allows one, starting from a crisp clustering of the text segments, to infer nuanced representations:

1) typicality of a text segment, relative to several semantic contexts, and not to a single one; 2) specificity (cue-validity) of each bigram in the diverse contexts; 3) dual relations between these indices, that do not exist to our knowledge with other crisp or fuzzy clustering methods.

C. Post-processing : the presentation of results

As will be detailed below, our unsupervised classification algorithm provides the ordered and valued lists of bigrams and characteristic documents of this cluster. To be able to interpret the theme dealt with in a cluster, additionally to documents titles, we must have the list of its most salient words (in our case: cartouches) available. The construction of the list for a given cluster requires to perform a 2nd pass on the documents of this cluster. For this reason, we extract altogether the bigram and its corresponding cartouche (i.e. phrase delimited by 2 blank spaces and which sequencial number in the original text corresponds to that of the current text unit). 3 It follows straightfully from the properties of eigenvectors that the first eigenvector of the inter-row cosine table D

-1 2 r X 1 2 X 1 2 ′ D -1 2 r
is F 1 . This vector can be interpreted as the "eigenvector centralities" [START_REF] Brandes | Visual ranking of link structures[END_REF] of the nodes of the valued graph whose adjacency matrix is this cosine table.

Tables for the resulting clusters are presented by order of decreasing centrality of Maya phrases for each cluster. We gathered together bigrams corresponding to the same phrases.

V. EXPERIENCES AND RESULTS

Several series of experiments were performed. We present here only two, having in common the same pre-processing and unsupervised classification parameters, but with different corpus encoding methods: first without splitting complex ligature glyphs into developed encodings, and secondly splitting ligature forms into simpler elementary glyphs. The corresponding ligature decomposition table represents the exogenous information introduced for the second experiment.

After several tests, the number of requested clusters (10) appeared as a reasonable balance between the number of analyzed texts segments (215) and expected analysis precision. bigrams are established from elementary glyphs found within each Maya text cartouche, ignoring links with adjacent cartouches. With this pre-processing, Maya text cartouches containing one single glyphic element are ignored. Furthermore, as our experimentation targets text within the Maya codex and not its astronomical or calendar tables, we excluded Maya cartouches containing nothing but red digits (in vigesimal notation) of series 8xx ̠ ̡

... ̴ or black digits of series 9xx ΄ ... For example, the digits couple 808/917 Ε wa s ignored. On the contrary, combinations of a digit (series 8xx or 9xx) with a non numerical glyph are processed, including:

• dates of the 260 days tzolkin calendar round which combine a red digit from 1 to 13 with one of the 20 days in series 7xx °Ô | ® ... ˎ (as for example 807.704 ̧ȃ 7 Kan),

• dates in the 365 days haab year calendar including maya month names (as for example 908.411/515 Όȃ ƛ 8 Cumku), or • numbers associated with words in the text, that often correspond to names of deities (as for example 908.255/220 ΌÜ ÿ ).

A. Without exogenous information

Ligatures of elementary glyphs were not broken down into their constitutive elements and appear as individual glyphs. Table II presents a 46 bigram cluster in which 21 phrases or hieroglyphical words, coloured in red within cartouches in the table of Maya phrases and bigrams of the cluster. We present here the transcription, translation and corresponding segments of the corpus, ordered by centrality ranking and in the present state of Maya writing decipherment. Only the 14 phrases corresponding to several occurrences in the corpus are displayed.

We note that, linked to the foreground in this cluster, the Mayan terms of the cycles of Mayan long count are standing out, with Kin 1 day, Uinic 20 days, Tun / haab 360 days or 1 year, Katun 20 years, Baktun / pictun 400 years. The origin date 4 Ahau 8 Cumku ̤°̨ȃ ƛ , from Mayan long count, stands out less prominently. Different parts of the almanac of the Number snake in long count and table of the numerals of 91 days constitute the basics of this cluster (6 documents among 10 in the cluster), but half of the sections of this almanac is more or less missing there. Sections 61AB and 69A of the same structure, with very similar and parallel texts (dates in long count) are rather closely linked (almanac of the Number snake there considers long count and so does the table of the numerals of 91 days). A strong centrality is given to bigrams of sections 61AB and 69A, introducing this single case in the corpus, at the expense of other elements in the cluster. The section 31b of the almanac of mythical and historical dates is a summed up resumption of the previous almanac, and its inclusion in the cluster 1 is relevant.

Besides, we notice that the thematic sorting of the text segments in the clusters coincides well with their distribution in the different almanacs of the codex.

B. With exogenous information : splitting ligature glyphs into developed encodings

For a significant number of glyph forms (107 upon the 402 signs, except the figures, of the Mayan font), considering their global inclusion in a code, their link with their essential components is lost to our method of unsupervised classification, while it appears however visually straightaway. See for example: the global coding 455 LJ , and developed coding 454/111 LJ , which corresponds in fact to the fusion of two stacked glyphs o dž of linked bigram 454.111.

As for the previous experience, but in a more clear-cut way, the 10 required clusters bring to light with strong centrality terms carrying related notions, as does the Table III for cluster 5. The emergence of content clusters is made more specific by the decomposition of tying, which enriches the number of contexts and cases of glyphs which are not very frequent in the corpus (typically with less than 10 occurrences). Also, it allows to categorise better, in the context of the corpus, the grammatical affixes of the significant glyphs, when an affix as 030 -ah (the mark of the accomplished), is written merged with the verb which it concerns in a tying 374 / 318.030 ș or 318.030 ȍ , instead of being juxtaposed separately as ľ Ŷ or ľ .

VI. RELATED APPROACHES

Besides the pioneering work of [START_REF] Évréïnov | Primenenie elektronikh vychislitel'nykh mashin v issledovanii pis'mennosti drevhikh mayia [Utilisation des machines calculer électroniques pour les recherches sur l'écriture des anciens mayas[END_REF], we are not aware of any data mining studies of Mayan texts other than ours. However, data mining approaches to Chinese texts present both strong similarities and strong differences:

-Considered at the graphical and structural levels, each chinese character can be portrayed as a "cartouche", i.e. a 2-dimensional display of semantic or phonetic components, among which 214 semantic "keys", and/or as a composition or repetition of other characters, resulting in a complex description [START_REF] Zucker | Learning structurally indeterminate clauses[END_REF], not unrelated to the above-described compositional aspects of Mayan cartouches: these components are distorted so as to fit the entire Chinese character into a square.

-These "cartouches" have been historically frozen into a large, but finite, number of well-specified characters: a few ten thousand characters listed in usual dictionaries and now computer-encoded, and a long distribution tail of rare ones, including hapax and variants, summing up to about 100 000.

-As a consequence, and given the lack of explicit separation marks between words, most Chinese search engines and many data mining studies, such as [START_REF] Zhou | A chinese document categorization system without dictionary support and segmentation processing[END_REF], [START_REF] Wei | Feature selection on chinese text classification using character ngrams[END_REF], [START_REF] Wei | Avancée en classification multi-labels de textes en langue chinoise[END_REF] use character n-grams as elementary features for coding Chinese texts, mainly 1-grams to 3-grams.

-These studies use, as we do, a vector count of ngrams for computing similarities between texts. The big difference is that they can use immense corpuses of many ten thousand news articles or Web pages, compared to the restricted exhaustive Mayan Corpus of three codices and a few thousand ceramic and monumental inscriptions.

- [START_REF] Wei | Avancée en classification multi-labels de textes en langue chinoise[END_REF] builds his supervised categorization of Chinese Web pages on a variant of the unsupervised Latent Dirichlet Allocation clustering method [START_REF] Blei | Latent dirichlet allocation[END_REF], which shares the same drawbacks of our Kmeans-based method: the process is initialization-dependant, and the number K of clusters has to be specified.

VII. CONCLUSION AND PERSPECTIVES

The coding of the Dresden codex under mayaT E X permitted to initiate a series of experiments highlighting semantic clusters through non-supervised learning. A cluster analysis giving nuanced results, thanks to our original method, was performed, based on the text division in page segments, characterized by their Maya bigram profile. This analysis confirmed the grouping of well understood glyphs into already known semantic clusters, and for other glyphs, more subject to controversy, permitted to orient their interpretation in a direction rather than other ones. A second experiment was performed, introducing knowledge components external to the corpus, i.e. the decomposition in simple glyphs of ligature glyphs, that confirmed the validity of this decomposition and allowed to reinforce the precision of the performed semantic division.

To refine the methodology, a number of variants remain to explore. On the one hand, by changing parameters in the processing chain: changing N, combining 1-grams and 2-grams, exploring other granularity levels for text statistical units such as sentences or cartouches instead of page segments, including n-grams that cross over the borders of 2 successive cartouches, in order to enlighten syntax structure and contexts. On the other hand, by modifying the corpus, i.e. selecting of a homogeneous and continuous subcorpus as Venus stage tables, or approaching the contexts of a Maya phrase to be deciphered by selecting the text segments containing it as a sub-corpus; or extending the corpus to the codices of Madrid and Paris, and even to inscriptions on ceramics, bringing light on rare glyphs thanks to other contexts. We also plan to test other methodological approaches characterizing texts by "pseudo-n-grams" or Triggers [START_REF] Lau | Maximum likelihood maximum entropy trigger language model[END_REF], relaxing the n-grams strict consecutiveness constraint; or also using glyph itemsets4 [START_REF] Cadot | Simuler et épurer pour extraire des motifs pertinents[END_REF], which would relax the sequentiality constraint inside the cartouches, while preserving inter-cartouche sequentiality. These first experiments encourage us to continue further in this direction. Indeed, no breakthrough has emerged from such partial and experimental results, but it appears that a stabilized procedure validated on the whole Maya corpus (the three codices and the ceramics and monument inscriptions) might induce a significant progress in the proportion of welldeciphered glyphs.

This case study illustrates the importance of mining homogeneous semantic contexts out of the data, respectful of both the diverse salience levels, or centralities, of the considered units (features, objects, individuals,...), and tolerant to some degree of polysemy -a central element in a given context may display significant projections in other contexts. Out of linguistic applications, many domains may benefit from this cognition-friendly type of analysis: among other topics, we have applied this methodology to delineating scientific fields and trends, on the basis of cocitation networks [START_REF] Bassecoulard | Mapping nanosciences by citation flows: a preliminary analysis[END_REF], as well as co-word analysis, or both [START_REF] Zitt | Hybrid citationword representations in science mapping: portolan charts of research fields ?[END_REF], by mining large subsets of bibliographic databases.

Another important methodological progress should come when getting rid of the drawbacks of most K-means or probabilistic clustering methods, i.e. initialization-dependance, and the need to determine the "right" number of clusters to be extracted. We have drawn up perspectives in that direction in recent papers of ours: in [START_REF] Lelu | Classification dynamique d'un flux documentaire : une évaluation statique préalable de l'algorithme GERMEN[END_REF] and [START_REF] Cuxac | Incremental analysis of the evolution of an indexed database: an assessment/correction loop for the choice of algorithms and parameters[END_REF] we have set up an initialization-independent density clustering method; in [START_REF] Lelu | Slimming down a high-dimensional binary datatable: relevant eigen-subspace and substantial content[END_REF] and [START_REF] Lelu | Espace intrinsèque d'un graphe et recherche de communautés[END_REF] we have described a statistically rigorous randomization test for establishing the intrinsic dimention of a binary dataset, which amounts to the upper bound of the number of clusters in the case of sparse binary data. The present work could then be considered as a feasability study in view of an exhaustive processing of the whole Mayan corpus, incorporating our recent advances and resulting in a stable basis for documenting the discussions on controversial or unknown glyphs in the Mayanist community.

Figure 2 .Figure 3 .

 23 Figure 2. Characterizing folio segments in the Dresde codex; x-axis, number of sentences in a segment; y-axis, number of segments. For example, one may read: 81 segments consist of 3 sentences

Figure 4 .

 4 Figure 4. Characterizing folio segments in the Dresden codex -Histogram of the number of glyphs per corpus segment: x-axis, number of individual glyphs in each segment; y-axis, number of corresponding segments in the corpus. For example, one may read: 73 folio segments consist of 30 to 39 individual glyphs.

  They fall into three main types. The logogram, or morphemic sign with both semantic and phonetic values, most often monosyllabic of the consonant-vocal-consonant (CVC) form, as glyph 204 Ì representing a four petals flower, symbol of the sun and with phonetic value KIN sun, day. The syllabogram, noting a CV or VC type syllable, as glyph +176 ° w ith phonetic value la which is used to write different words combined with another syllabogram or a logogram as +176/204 Ì ° l a-KIN (East). Syllabograms are derived from CV(C) value logograms in which the second consonant is weak. The phonetic complement, a sign of phonetic value CV, VC or a part of the C(V) value of the logogram to which it is associated, as in the word 204.031 Ì , where 031 is the phonetic complement ni or in, postfixed to KIN (the sun, day) to confirm the reading spelling. A word can be written through different combinations of glyphs that note the same phonetic value, as for lakin (East) indifferently written by allographs +176/204 Ì ° , 176/204.031 Ì ° , 204/176.031 °Ì or 031.+176/204 Ì °

  may differ: e.g. the three variants 032.063/153 ?

Table II CLUSTER

 II 1 MAYA TERMS BY DECREASING CENTRALITY. DRESDEN CODEX ENCODED WITHOUT SPLITTING LIGATURES INTO ELEMENTARY GLYPHS

	Rank	Maya term	Colonial Yucatec	Meaning and translation	Corresponding folio segments
				transcription
	1	Ŭ 364/(153.153)	baktun / pictun	20 x20 x18 x20 = 144.000 days	D61AB, D69A
	2	ǹ ł ǹ Ē ǹ E ǹ E	069c/(-505.274.-505) 069/(-505.322.-505)	pawah thul pawah cizin	cycle, i.e. 400 years sure] divinity rabbit divinity death [un-	D61AB, D69A
	3	p	173/112	uinic	man, 20 days cycle	D61AB, D69A
	4	Ü	023.153.023)/220	katun	20 years 20X18x20=7.200 days cycle, i.e.	D61AB, D69A
	5	Ü 220/009	tun/haab	18x20=360 days cycle, solar year	D61AB, D69A
					(360+5 jours "unnamed" inter-
					calary days)
	6	i	105/155.030	pat otoch-ah / pat-ah /	place into the house/to form	D52b, D61AB, D69A
				kat-ah
	7	6Ô 054.212	och ixim/ha'	enter [into] maize/water	D31a, D61AB
	8	Ô 8	056/212	ti ixim/ha'	into maize/water	D51a, D52a, D61AB, D69B
	9	ˁ <	060/?705.030	o chicchan-ah	[not understood]	D61AB
	10	Ì 204/031	kin	day, sun	D61AB
	11	õë 245.235	yax Ahau	the green lord	D61AB, D69A
	12	̤°8 04.700	chan ahau	dar date] l4 Ahau [260 days Tzolkin calen-	D31a, D51b, D69A, D70b
	13	ȃ ƛ 411/515	cumku	Maya month Cumku	D31a
	14	K Ĭ 075.300/031	yoon / yoon kin	parents of the sun [unsure]	D61AB, D69A

Table III HIGHEST

 III CENTRALITY MAYA TERMS FOR CLUSTER 5. DRESDEN CODEX WITH LIGATURE GLYPHS SPLITTED INTO DEVELOPED ENCODINGS.

Rank Maya terms of highest centrality Colonial Yucatec transcription Meaning / Theme Number of bigrams in the cluster

	1	Ü	̧ȃ	tun/haab 8 Kan	year, date in the 260 days	19
		220/009	807.704		tzolkin calendar
	2	̩®	Ώ	9 Akbal 11 Chuen	dates in the 260 days	23
		809.703	911.711		tzolkin calendar
	3	Ĕ	C ij Ǹ	cimi, kam	death	14
		276/010	307/067.504
	4	¬	"ç	u-muc, Ixchel,	its omen, moon divinity	22
		026.172/023	034.319.034/135
	5	d	{ ±	zih-an, ahau dzak	born from, accession to
		(076.234.076)/024	(154.123)/177		power

In this respect our methodology differs from "fuzzy clustering"[START_REF] Bezdek | Optimal fuzzy partition: A heuristic for estimating the parameters in a mixture of normal distributions[END_REF], because the sum of the centralities of a statistical unit in the different clusters is not forced to 1; here centrality does not convey the uncertainty of the belonging to a cluster (a probability), but a contribution to context building.

A set of two to n glyphs, non necessarily consecutive nor ordered within the same textual unit, for example the cartouche.


MD Jean-Bernard Gouyon
email: jean-bernard.gouyon@chu-dijon.fr

Amelie Vintejoux

Paul Sagot

Antoine Burguet

Catherine Quantin

Cyril Ferdynus

Bernard

Vintejoux A Md

PHD, * §Burguet A MD P Md

PHD Quantin C Md

Ms

Neonatal outcome associated

Keywords: Late-preterm, respiratory disorders, poor prognosis, early-term, late-term, mortality

teaching and research institutions in France or abroad, or from public or private research centers.

Background: Approximately 75% of preterm births are late-preterm (34 0/7 to 36 6/7 weeks' gestation). This group has usually been considered as a whole in studies assessing the outcome of these preterm infants by comparison with term infants. However, the respective contribution to prognosis of each week of gestation has not been fully clarified.

Methods: A population-based study of 150,426 live-born singleton neonates with gestational ages ranging from 34 to 41 weeks of gestation.

Results:

The rate of severe respiratory disorders (treated by mechanical ventilation and/or nasal continuous positive airway pressure) markedly declined with gestational age from [START_REF] Platt | Detecting and eliminating erroneous gestational ages: a normal mixture model[END_REF].8% at 34 weeks to 0.28% at 39-41 weeks. Between 34 to 38 weeks, each additional week diminished the relative risk (crude or adjusted) of severe respiratory disorders by a factor varying from 2 to 3. The rate of poor prognosis (death and/or severe neurological condition) significantly declined between 34 to 38 weeks and remained stable thereafter. A multivariate analysis showed that antepartum hemorrhage and hypertensive disorders during pregnancy were significantly associated with severe respiratory disorders and poor outcome. Diabetes was an additional factor associated with severe respiratory disorders.

Conclusions: Future studies should delineate more precisely the respective contribution of gestational age, maternal complication and induced delivery in the prognosis of infants born between 33 and 39 weeks' gestation.

KEY WORDS

Late-preterm; early-term; late-term; respiratory disorders; mortality; poor prognosis.

INTRODUCTION

The preterm birth rate has increased in developed countries over the past decade [START_REF] Engle | Late preterm infants, early term infants, and timing of elective deliveries[END_REF] and the US rate reached 12.7% in 2005 [START_REF] Martin | Births: final data for 2005[END_REF]. Most studies have focused on infants born before 33 weeks of gestation because they are at high risk of mortality and serious morbidity. However, approximately 75% of preterm births are late-preterm (34 0/7 to 36 6/7 weeks of gestation) (3).

Late-preterm infants are 3.5 times more likely to have clinical problems than term infants and their neonatal mortality is 4.6 times higher (4). Therefore, these infants represent a substantial proportion of hospitalizations after delivery [START_REF] Escobar | Rehospitalisation after birth hospitalisation: patterns among infants of all gestations[END_REF]. The outcome of late-preterm infants can be related to physiological immaturity but also to maternal complications leading to a preterm birth (6, 7), a condition making the antenatal assessment of prognosis more difficult.

Moreover, early-term neonates (37 0/7 to 38 6/7 weeks' gestation) account for 17.5% of live born infants [START_REF] Hankins | Cesarean section on request at 39 weeks: impact on shoulder dystocia, fetal trauma, neonatal encephalopathy, and intrauterine fetal demise[END_REF] and were found to experience more transient tachypnea of the newborn, persistent pulmonary hypertension and a longer hospital stay than infants born at 39 weeks of gestation (9 -13).

Even though a continuum for both mortality and morbidity according to gestational age has been underlined by the National Institute of Child Health and Human Development [START_REF] Raju | Optimizing care and outcome for latepreterm (near-term) infants: a summary of the workshop sponsored by the National Institute of Child Health and Human Development[END_REF], the respective contribution to prognosis of each week above 33 weeks' gestation has not been fully clarified, as recently pointed out by Kashu et al. [START_REF] Khashu | Perinatal outcomes associated with preterm birth at 33 to 36 weeks'gestation: a population-based cohort study[END_REF]. Analysis of perinatal morbidities, on the basis of each week of gestation rather than grouping infants by weeks of gestation at delivery (as late-preterm, early-term and late-term infants) could be more relevant.

Therefore, the aim of this study was to assess the neonatal outcome associated with each week of gestational age over 33 weeks. Data on the population of all mother-infant pairs cared for in Burgundy hospitals between January 1, 2000, and December 31, 2008, were obtained from a regional database which was set up with the approval of the National Commission for Data Protection (CNIL ## 98003718). The Burgundy perinatal data system is a longitudinally linked data system of mothers and their children up to discharge from maternity and neonatal units [START_REF] Cornet | Using discharge abstracts as a tool to assess a regional perinatal network[END_REF][START_REF] Quantin | Using discharge abstracts to evaluate a regional perinatal network: assessment of the linkage procedure of anonymous data[END_REF]. The list of variables under study included those presented in Tables 1 and2, congenital malformations and multiplicity. The gestational age in completed weeks was assessed on the basis of the mother's last menstrual period, as confirmed or modified when necessary by routine early antenatal ultrasound examination. In Burgundy, as in other French regions, 90% of pregnant women experience an early ultrasound examination [START_REF] Blondel | Résultats des enquêtes périnatales[END_REF]. 'Data on gestational age was missing in 0.30% of cases. Moreover, gestational age was implausible considering birth weight in 0.37%, using a method developed by Platt et al. [START_REF] Platt | Detecting and eliminating erroneous gestational ages: a normal mixture model[END_REF]. Corrections regarding implausible gestational ages were obtained from medical files.

Multi-fetal births, severe congenital malformations, chromosomal abnormalities and metabolic diseases were not included in the study because gestational age -related morbidity and mortality in those infants significantly differ from that of singletons [START_REF] Mcintire | Neonatal mortality and morbidity rates in late-preterm births compared with births at term[END_REF][START_REF] Young | Mortality of late-preterm (near-term) newborns in Utah[END_REF].

F o r R e v i e w O n l y

Definitions Prematurity

Late-preterm, early-term and late-term infants were defined respectively by gestational age at 34 0/7 -36 6/7 ; 37 0/7 -38 6/7 ; 39 0/7 -41 6/7 weeks of gestation, [START_REF] Raju | Optimizing care and outcome for latepreterm (near-term) infants: a summary of the workshop sponsored by the National Institute of Child Health and Human Development[END_REF].

Maternal conditions

We examined maternal age and complications of pregnancy including hypertensive diseases of pregnancy (combining chronic hypertension, pregnancy-induced hypertension, preeclampsia and eclampsia), diabetes (combining gestational and established diabetes), placental abruption, placenta praevia, preterm and premature rupture of membranes (PPROM), antenatal diagnosis of fetal weight restriction and chorioamnionitis.

Premature rupture of membranes was defined by rupture of membranes before the first stage of labour (by more than 18 hours). PPROM referred to rupture of membranes before 37 weeks of gestation.

Chorioamnionitis was defined as infection or suspected infection of the amniotic cavity as determined by clinical criteria by the attending physician.

Small-for-gestational-age newborns were identified when birth weight was below the 10 th percentile according to neonatal growth standards based on a healthy population of mothers [START_REF] Ferdynus | Can birth weight standards based on healthy populations improve the identification of small-for-gestational-age newborns at risk of adverse neonatal outcomes?[END_REF].

Birth conditions

Abnormal fetal heart rate recordings, mode of delivery (vaginal or caesarean section) and instrumental maneuvers at delivery were recorded. Asphyxia at birth was defined as an Apgar score below or equal to 3 at 1 min of life. Severe respiratory disorder was defined as a respiratory distress treated by mechanical ventilation and/or nasal continuous positive airway pressure.

Statistical Analyses

Qualitative variables were presented as percentages and continuous variables as mean and standard deviations.

DISCUSSION

This study confirmed that late-preterm infants (34 0/7 to 36 6/7 WG) were more likely to have severe respiratory disorders (i.e. treated with ventilator and/or nasal continuous positive airway pressure) and poor prognosis than late-term infants born at 39-41 weeks of gestation.

Furthermore, this study provided important additional information showing that: birth at 37 weeks of gestation was associated with an increased incidence of poor prognosis; infants born at 37 and 38 weeks of gestation were at increased risk of severe respiratory disorders; up until The strengths of this study lie in the large population-based cohort of infants and an analysis by week of gestation. However, its limitation was the retrospective analysis of maternal and neonatal data, collected prospectively. That condition was previously associated with a lack of sufficient information on antenatal corticosteroids (1). The 9 year-period of this study might have been associated with slight changes in clinical practice. However, the study period has not been associated with overt changes in clinical practice or changes in the distribution of gestational age in this regional population.

In this study, the incidence of severe respiratory conditions steadily decreased from the latepreterm group (8.3%), to the early-term group (0.84%) and to the late-term group (0.28%).

This data matches the gestational age-related decline in incidence of respiratory disorders (respiratory distress syndrome, transient tachypnea of the newborn, persistent pulmonary hypertension) and need for mechanical ventilation reported in previous epidemiological studies (11; 24 -27). This trend may be illustrated by comparison to incidences recorded in the United States [START_REF] Escobar | Short-term outcomes of infants born at 35 and 36 weeks gestation: we need to ask more questions[END_REF] and Italy [START_REF] Rubaltelli | Epidemiology of neonatal acute respiratory disorders. A multicenter study on incidence and fatality rates of neonatal acute respiratory disorders according to gestational age, maternal age, pregnancy complications and type of delivery. Italian Group of Neonatal Pneumology[END_REF]: respectively 20.6% and 22.1% among babies born at 33-34 weeks; 7.3 and 8.3% at 35-36 weeks; 0.6 and 2.9% at 37-42 weeks.

Compared to at term infants (37-40 weeks), the occurrence of respiratory distress has been previously evaluated at 4.5-fold higher in the 33-36 week infants ( 15) and even at 9.1-fold higher in the 35-36 week infants [START_REF] Wang | Clinical outcomes of near-term infants[END_REF]. Compared with late-term infants (39-41 weeks), the adjusted relative risk for severe respiratory disorders in this study was 2.7 in early-term and 23.9 in late-preterm infants. These results suggest that the risk for respiratory morbidity in late-preterm infants has been previously underestimated because early-term infants were included in the control group. This study also showed that the rate of severe respiratory diseases approximately doubled for each reduced week of gestation from 39 to 34 weeks. Similarly, Shapiro-Mendoza et al. [START_REF] Shapiro-Mendoza | Effect of late-preterm birth and maternal medical conditions on newborn morbidity risk[END_REF] also observed that the rate of life-threatening conditions doubled for each reduced week of gestation before 38 weeks' gestation. The Kaiser Permanente Cohort showed that an increased risk of respiratory disease was associated with decreasing gestational age before 37 weeks (9), while our cohort disclosed that an increased risk of severe respiratory disease was still apparent at 38 weeks. These overall data strongly support that birth before 39 weeks of gestation cannot be considered as low-risk, and emphasize the need to consider each week of gestation separately.

This study found that the incidence of poor prognosis (severe neurological disease and/or death) was not higher at 38 weeks, while it increased steadily below 38. Furthermore, a 3.5fold higher poor prognosis was observed in the late-preterm group compared to the late-term group. Sources from Canada (29), the Unites States and Europe (15, 30 -32) disclosed comparable profiles for gestation-specific neonatal mortality rates. For instance, a Canadian study [START_REF] Khashu | Perinatal outcomes associated with preterm birth at 33 to 36 weeks'gestation: a population-based cohort study[END_REF] found that the neonatal mortality rate was 5.5 times higher in a 33-36 week group compared with a 37-40 week group. Another study [START_REF] Joseph | A parsimonious explanation for intersecting perinatal mortality curves: understanding the effect of plurality and of parity[END_REF] highlighted that mortality in the latepreterm group contributed to 10 % of overall neonatal mortality, a finding close to the 12.2% observed in the Burgundy population (personal data).

Recently, Shapiro-Mendoza et al. ( 7) contributed important information by showing that both late-preterm birth and, to a lesser extent, maternal medical conditions are each independent risk factors for severe newborn morbidity, especially when late-preterm infants have been exposed to antepartum hemorrhage and hypertensive disorders of pregnancy. Using a more precise classification of clinical neonatal conditions, our study confirmed that antepartum hemorrhage and hypertensive disorders of pregnancy were associated with severe respiratory The need for admission in a neonatal unit linearly increased from 39-41 weeks of gestational age (5.8%) to 37 weeks (17.8%) and to 34 weeks (96.9%). Similarly, a large epidemiological study conducted in the United States previously found an increase in the neonatal unit admission rate from 2.6% in infants born at 38-40 weeks to 12% at 37 weeks of gestation and 88% at 34 weeks [START_REF] Escobar | Rehospitalisation after birth hospitalisation: patterns among infants of all gestations[END_REF]. It can be assumed that the differences in absolute rates of admission between the studies may result from different care systems at national or regional levels.

F

  Neonatal outcome associated with singleton birth at 34 to 41 weeks of gestation.

METHODS

  We used a population-based cohort of neonates delivered in all hospitals of Burgundy, a French region with approximately 18,000 births per year. The perinatal network of Burgundy included 18 public and private hospitals that were categorized into 3 levels: (a) level III for neonatal intensive care (n = 1); (b) level II for high dependency care (n = 7); and (c) level I for normal care (n = 10).

Outcomes

  Poor prognosis was defined at the end of neonatal hospitalization by death and/or severe neurological condition (ischemic encephalopathy; intraventricular hemorrhage grades 3-4 according to Papile et al.[START_REF] Papile | Incidence and evolution of subependymal and intraventricular hemorrhage: a study of infants with birthweight less than 1500 gm[END_REF] and/or cystic periventricular leukomalacia in preterm infants and/or seizures). Transfontanelar echography was systematically performed in newborns with neurological symptoms.

  gestation, each additional week contributed to improve the clinical condition of the newborns.

  prognosis. Diabetes was an additional factor associated with severe respiratory distress.

*

  Poor prognosis = death and/or severe neurological condition at the end of neonatal hospitalization. ** Severe respiratory disorder = respiratory distress treated by mechanical ventilation and/or nasal continuous positive airway pressure.

  weeks of gestation was associated with an increased incidence of poor prognosis; Infants born at 37 and 38 weeks of gestation were at increased risk of severe respiratory disorders;Before 39 weeks of gestation, each additional week contributed to improve the clinical condition of the newborns.

Table 2

 2 shows crude and adjusted relative risks for the two outcomes. Between 34 and 37 weeks of gestation, the risk of poor prognosis gradually diminished, but nevertheless remained higher than for infants born at 39-41 weeks of gestational age. Even after diseases, the risk of poor prognosis was higher (aRR= 1.6; 95% CI = 1.1 -2.3) at 37 weeks of gestation compared with infants born at 39-41 weeks. The adjusted relative risk for poor prognosis was 3.6 (95 % CI: 2.5 -5.3) in late-preterm infants and 1.1 (95% CI: 0.8 -1.4) in early-term infants, compared with the late-term infants.Between 34 and 38 weeks, each additional week decreased the relative risk (crude or adjusted) of severe respiratory disorders by a factor varying from 2 to 3 (Table2). The adjusted relative risk for severe respiratory disorders was 23.9 (95% CI: 20.5 -27.8) in latepreterm infants and 2.7 (95% CI: 2.3 -3.2) in early-term, compared with late-term infants.Poor prognosis was associated with severe respiratory disorders in 37.5% for latepreterm, 37.5% for early-term and 19.7% for late-term infants. The rate of poor prognosis among the neonates with severe respiratory disorders was 6.8% versus 0.1% in infants without respiratory disorders (p < 0.0001).

	05. First order

Bivariate analyses were conducted using chi-square test or Fisher's exact test for comparisons of percentages, and Student's t-test or Mann-Whitney's test for comparisons of means.

Multivariate analyses were conducted using modified Poisson regression models

[START_REF] Zou | A modified poisson regression approach to prospective studies with binary data[END_REF]

with correction for overdispersion, separately for each outcome. The final multivariate models were obtained using backward selection procedure. The covariates with a p-value ≤ 0.20 in bivariate analyses, and covariates considered as risk factors in the literature, were included in the initial model, and removed if they did not reach a p-value below 0.

Statistical analyses were performed using SAS 8.2 (SAS Institute Inc).

The incidence of all antenatal complications declined linearly from 34 to 39-41 weeks of gestation. The incidence of mothers without gestational complication was significantly different among the late-preterm, early-term and late-term groups (43.4% vs 69.6% vs 84.2%, p < 0.0001). Gestational age was positively correlated with vaginal delivery with or without instrumental maneuver and negatively correlated with emergency caesarean section (p < 0.0001).

Figure

1

shows the rates of severe respiratory disorders and poor prognosis for each week of gestational age. A poor prognosis was recorded in 0.80% of late-preterm infants, 0.18% of early-term infants and 0.16% of late-term infants (p < 0.0001). When examining each week of gestation, the rate of poor prognosis significantly declined from 1.

Table 1 : Characteristics of live-born singleton neonates with gestational age ranging from 34 to 41 weeks of gestation

 1 This study confirmed that late-preterm infants are a population at risk of increased respiratory morbidity and poor prognosis, while an intermediate risk of respiratory morbidity was observed in the early-term infants. Therefore birth at 37 and 38 weeks of gestation is not lowrisk for the newborn, and this information should lead to avoidance of caesarean section or labor induction without medical indication in early-term infants as well as in late-preterm infants.The continuous pattern of improvement from one week to the following is a limitation of the current terminology which delineates late-preterm, early-term and late-term infants. Future studies should identify more precisely the respective contribution of each week of gestation, of maternal complications and of induced delivery in the prognosis of infants born between 34 and 39 weeks of gestation.

	CONCLUSIONS
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Table 2 : Crude and adjusted relative risks for severe respiratory disorders and poor prognosis according to gestational age, gender and maternal conditions.

 2 Poor prognosis = death and/or severe neurological condition at the end of neonatal hospitalization. ** Severe respiratory disorder = respiratory distress treated by mechanical ventilation and/or nasal continuous positive airway pressure. cRR = Crude Relative Risk. aRR = Adjusted Relative Risk, calculated only for covariates present in the final multivariate model. CI = Confidence Intervals. HDP = Hypertension Disease of Pregnancy. PPROM = Preterm and Premature Rupture of Membranes. NA = Non Applicable.

			Poor prognosis			Severe Respiratory Disorders
		cRR	95% CI	aRR	95% CI	cRR	95% CI	aRR	95% CI
	34 weeks	10.5	6.7 -16.6	6.8	4.1 -11.1	68.6	54.1 -86.9	61.0	49.7 -74.8
	35 weeks	4.2	2.4 -7.2	3.0	1.7 -5.2	33.6	26.2 -43.1	31.0	25.1 -38.3
	36 weeks	3.9	2.6 -5.8	3.1	2.1 -4.7	15.3	11.9 -19.7	14.2	11.6 -17.4
	37 weeks	1.7	1.2 -5.5	1.6	1.1 -2.3	4.9	3.8 -6.5	4.7	3.8 -5.8
	38 weeks	0.9	0.7 -1.3	0.9	0.6 -1.2	2.1	1.7 -2.8	2.1	1.7 -2.5
	39-41 weeks	1.0	-	1.0	-	1.0	-	1.0	-
	Maternal Age, years
	< 20	1.2	0.6 -2.4	NA	NA	1.1	0.8 -1.6	NA	NA
	20-24	1.0	0.7 -1.4	NA	NA	0.8	0.7 -1.1	NA	NA
	25-29	1.0	-	NA	NA	1.0	-	NA	NA
	30-34	1.0	0.8 -1.4	NA	NA	1.1	0.9 -1.2	NA	NA
	35-39	0.9	0.6 -1.4	NA	NA	1.2	1.0 -1.5	NA	NA
	≥ 40	1.3	0.7 -2.7	NA	NA	1.5	1.1 -2.1	NA	NA
	Gender, Male	1.3	1.1 -1.6	1.3	1.0 -1.6	1.5	1.4 -1.7	1.5	1.3 -1.6
	HDP	2.2	1.5 -3.4	1.6	1.1 -2.5	4.1	3.4 -4.8	1.4	1.2 -1.7
	Preterm labour	1.4	0.9 -2.2	NA	NA	3.1	2.6 -3.7	NA	NA
	PPROM	0.9	0.5 -1.4	NA	NA	2.0	1.7 -2.4	NA	NA
	Antepartum hemorrhage	13.0	7.6 -22.5	6.3	3.5 -11.3	15.2	11.5 -20.8	2.4	1.8 -3.2
	Clinical chorioamnionitis	3.1	0.4 -22.1	NA	NA	6.7	3.3 -13.6	NA	NA
	Diabetes	1.4	0.8 -2.2	NA	NA	2.4	1.9 -2.9	1.5	1.2 -1.9
	*

19 Figure 1: Proportions of newborns with severe respiratory disorders and poor prognosis, according to gestational age.

	20.0%	19.83%
	15.0%
	10.0%		9.67%
										8.31%
	5.0%			4.44%
		1.69%			1.42%
			0.66%	0.62%	0.27%	0.15%	0.62%	0.16%	0.28%	0.80%	0.84% 0.18%	0.16%	0.28%
	0.0%
		34	35	36	37	38	39-41	Late	Early	Late
		weeks	weeks	weeks	weeks	weeks	weeks	Preterm	Term	Term
				Poor prognosis Severe respiratory disorders

ACKNOWLEDGEMENTS

The authors wish to thank the members of the Burgundy perinatal network and all physicians in hospitals of the Burgundy region (CH de Sens, Auxerre, Nevers, Dijon, Beaune, Chalonsur-Saône, Mâcon, Montceau-les-Mines, Paray-le-Monial, Le Creusot, Semur-en-Auxois, Chatillon-sur-Seine, Autun, Decize ; clinique Sainte-Marthe, clinique de Chenôve, clinique d'Auxerre et clinique du Nohain).

FUNDING

This work was supported by "Union Régionale des Caisses d'Assurance Maladie" and l'Agence Régionale d'Hospitalisation" of Burgundy (grant : FIQCSV 11-04-08).