Ali Harb
email: harb@emse.fr

Michel Beigbeder

Kristine Lund
email: kristine.lund@univ-lyon2.fr

Jean-Jacques Girardot
email: girardot@emse.fr

A Harb Is A Phd

Jean-Jacuqes Girardot

Jean-Jacques Girardot

Enhanced semantic expansion for question classification

Keywords: classification, feature selection, semantic expansion, mutual information, MI, machine learning, text mining

Most question and answering systems are based on three research themes: question classification and analysis, document retrieval and answer extraction. The performance in every stage affects the final result. To respond correctly to a question given a large collection of textual data is not an easy task. There is a need to perceive and recognise the question at a level that permits to detect some constraints that the question imposes on possible answers. The classification of questions appears as an important task because it deduces the type of expected answers. The purpose is to provide additional information to reduce the gap between answer and question. A method to improve the performance of question classification focusing on linguistic analysis and statistical approaches is presented. This work also proposes two methods of questions expansion. Various questions representation, term weighting and diverse machine learning algorithms are studied. Experiments conducted on actual data are presented. Of interest is the improvement in the precision on the classification of questions.

Introduction

With the ongoing expansion of the web, the number of documents becomes increasingly both significant and considerable. During an information search, the user is faced with numerous documents returned by search engines, many of which are not relevant. Question answering (QA) systems are viewed as a way to rapidly deliver information, particularly in response to specific questions. Classifying the questions to anticipate the type of answer is a very important step in an effective QA system. This useful task appreciably reduces the search space to identify the correct answer and improves the quality of service.

Traditionally, many QA systems use manually constructed rules [START_REF] Kosseim | Improving the performance of question answering with semantically equivalent answer patterns[END_REF][START_REF] Plamondon | The QUANTUM question answering system[END_REF][START_REF] Kangavari | A new model for question answering systems[END_REF][START_REF] Saxena | IITD-IBMIRL system for question answering using pattern matching, semantic type and semantic category recognition[END_REF] to typify the questions, which is not very efficient for maintenance and upgrading. Recently, with the growing popularity of statistical approaches, machine learning was applied to detect the categories of questions [START_REF] Harb | Evaluation of question classification systems using differing features[END_REF][START_REF] Krishnan | Answer type inference from questions using sequential models[END_REF][START_REF] Hacioglu | Question classification with support vector machines and error correcting codes[END_REF][START_REF] Zhang | Question classification using support vector machines[END_REF][START_REF] Li | Learning question classifiers: the role of semantic information[END_REF][START_REF] Fu | Two level question classification based on SVM and question semantic similarity[END_REF]. The advantage is that machine learning algorithms can recognise among discriminating features, and rely on the learning process to efficiently cope with the features. The bag-of-words (BOW) representation is frequently used in the classification tasks using machine learning. However, where the questions are short, we need to combine many features in question representation and to add relevant information to let classifiers achieve higher precision.

In this work, several possible semantic information sources will be described that differ in their granularity and method of acquisition. Then, these new enhanced sources will fill-out the semantic sense of the questions. For instance, this integration should help to obtain the grammatical category of terms (noun, verb, adjective, etc.), the semantic categories of nouns (e.g., person, location), or synonyms, hypernyms, hyponyms of nouns. The actual sense of terms must be retained and for this we will use their context.

The paper is organised as follows: Section 2 describes the principal techniques used in question classification. In Section 3, we present a study on the different features used in question representation. Section 4 details the experiments conducted on various features with three learning algorithms. Our approach is summarised in Section 5, where we will describe the general expansion method. Section 6 presents the experimental results conducted on actual data.

Related work

Question classification approaches can be divided into two main groups: one composed of manually constructed sets of rules and the other based on machine learning. In the former hand written grammar rules are used to parse a question and to extract significant patterns [START_REF] Kosseim | Improving the performance of question answering with semantically equivalent answer patterns[END_REF]. The QUANTUM system, [START_REF] Plamondon | The QUANTUM question answering system[END_REF] define a set of 40 rules which properly classifies 88% of the 492 questions collected from TREC-10. The systems described in [START_REF] Kangavari | A new model for question answering systems[END_REF] and [START_REF] Saxena | IITD-IBMIRL system for question answering using pattern matching, semantic type and semantic category recognition[END_REF] use a set of rules based on the determinant words (e.g., who, where, ...). Thus, for each determinant word they build a special category question type (e.g., who questions are classified as requiring answer type person). Those manual rules are difficult and time consuming to construct. Their coverage is limited, because it is almost impossible to anticipate all the question categories. Thus, this influences the effectiveness of the entire QA system. During evolution of the taxonomy or when a new taxonomy is adopted, many previously prepared rules have to be scrapped, modified or completely rewritten.

In the latter group that uses machine learning expert knowledge is replaced by a learning corpus containing labelled questions. Using this corpus, a classifier is trained in a supervised mode. Possible choices of classifiers include but are not limited to: neural networks (NN), naive Bayes (NB), decision trees (DT), support vector machines (SVM) and K nearest-neighbours method (KNN). Reconstruction of a learned classifier is more flexible than of a manually constructed system because it can be trained on a new taxonomy in a short time. [START_REF] Zhang | Question classification using support vector machines[END_REF] compare a SVM-based classification system to other machine learning approaches (KNN, NB, and DT). All these classifiers use the BOW model and are trained on the same learning corpus. Recently, [START_REF] Li | Learning question classifiers[END_REF] used the SNoW learning architecture [START_REF] Khardon | Relational learning for NLP using linear threshold elements[END_REF] for question classification. They constructed the UIUC question classification corpus. In this work, they used part-of-speech tags, parsing, head chunks (first noun in a question) and named entities. They achieved 78.8% accuracy.

In recent years, numerous question taxonomies have been defined, however there is not a single standard used by all systems. Most of the participants in the TREC-10 campaign implement their own question taxonomy. Moreover, their taxonomy is frequently redefined from year to year. Usually, the systems use a taxonomy consisting of less than 20 question categories. However, as demonstrated by several QA systems, employing detailed taxonomy consisting of fine-grained categories is beneficial [START_REF] Zhang | Question classification using support vector machines[END_REF][START_REF] Li | Learning question classifiers[END_REF]. More recently, the taxonomy and corpus described in [START_REF] Li | Learning question classifiers: the role of semantic information[END_REF] has become the most frequently used in current research. [START_REF] Hacioglu | Question classification with support vector machines and error correcting codes[END_REF] describe a system using a support vector machine with word bigrams which obtains a precision of 80.2%. Most recently, [START_REF] Krishnan | Answer type inference from questions using sequential models[END_REF] used N-grams (N = 1 or 2) and integrated all the hypernyms of words and achieved 86.2% on the same corpus of questions with the same taxonomy. In the work of [START_REF] Fu | Two level question classification based on SVM and question semantic similarity[END_REF], they used a classifier based on SVM combined with a question semantic similarity. [START_REF] Harb | Evaluation of question classification systems using differing features[END_REF] describe a comparison between the performances of different classifiers. They extract discriminant words from question. Furthermore, they expand question by hypernyms. They achieved an accuracy of 80.9%. Later, in [START_REF] Li | Learning question classifiers: the role of semantic information[END_REF], they used more semantic information sources including named entities, WordNet and class specific related works. Using these, they were able to achieve the best accuracy 86.3%.

In this work, we propose to use a combination of known and new features. However, we will expand question with terms that preserve the actual sense of the original words. For this endeavour, we propose and test several types of semantical expansions and their combinations.

Features

In any automatic classification of text, the choice of the instance representation to be processed (in our case questions) and the operations to be applied is crucial. With the BOW representation the single information used is the presence or the frequency of certain words. Many researchers have chosen to use a vector depending on the Salton model [START_REF] Salton | Term-weighting approaches in automatic text retrieval[END_REF]. This representation transforms each question in a vector of n weighted words. Initially, the descriptors of the text may well simply be all the unique words in the documents. It is possible to use other types of features to characterise vectors, some of which will be presented later.

Our analysis revealed that some syntactic and semantic information that frequently exist in questions and belonging to the same category do not appear in the others. So, exploiting this information will provide valuable clues to classifiers to supplement the simple BOW approach.

Syntactic features

In addition to the words themselves, the syntactic features for each question include lemma, part-of-speech tag (verb, noun, adjective, etc.), the result of syntactic analysis and in particular grammatical dependencies. Significant words in sentence (e.g., object, subject, ...) can be detected with the use of grammatical dependencies.

Semantic relationships between words

Words can be related in several different ways. These relationships, in controlled vocabularies, can be categorised into many important classes such as: equivalency and hierarchy. The primary relation in the equivalency class is that of synonymy. Specifically, synonymy describes the relationship between two words that have the same conceptual meaning (e.g., city and town). In the hierarchy class, hypernymy describes the semantic relation of being superordinate or belonging to a higher class (e.g., flower and plant). The semantic information provides context-based knowledge of word meanings to any classification system and improve results.

Named entities

This feature assigns a semantic category to some nouns in the questions. The presence of those named entity tags in questions will favour the common semantic discriminant belonging to the same question type. (e.g., Who is the first president of France?, the named entity tagger will get: Who is the [Num first] [Vocation president] of [Country France]). As we can see, we obtain additional semantic information expressed in the categories of first (Number), president (Vocation) and France (Country).

N-grams

Words N-grams are sequences of N consecutive words. This model is founded on the assumption that the presence of a word is only relevant to the n words before and after it. It embodies the features of word order, and therefore, it can reflect the theme of the sentence more accurately than isolated words.

Term weighting

Let n be the total number of unique features (e.g., words, N-grams, etc.) in the corpus. Each question will be represented by a vector of n elements. Each component of this vector can simply be binary or can correspond to the number of occurrences of the feature in the question. However, using frequency accords too much importance to the features that appear very often in all question categories and are hardly representative of one category in particular. Another weight known as term frequency, inverse document frequency (TF.IDF). [START_REF] Salton | Term-weighting approaches in automatic text retrieval[END_REF] measures the importance of the words according to their frequency in the question (tf(t, d)) weighted by frequency of their occurrence in the entire corpus ( )

|| () () l o g . S df t idf t = (, ) (, ) () t f i d ftd t ftd i d ft ⋅= ⋅ (1)
| S | is the number of documents in the corpus and df(t) is the number of documents containing t. This of a question. Conversely, a term that appears in many questions will have a low weight.

Training set

We used a training set of 10,343 questions, which is a collection from the following: 5,500 UIUC DATA [START_REF] Li | Learning question classifiers[END_REF], 1,343 from (TREC10, TREC9, TREC8), 200 from QA@CLEF2006, 2,249 from CRL-QA and 1,011 from NTCIR-QAC1.

Taxonomy

Taxonomy proposed in [START_REF] Li | Learning question classifiers[END_REF] was chosen because it has a large coverage of question types and it represents a natural semantic classification for question types. It contains six coarse and 50 fine grained classes, shown in Table 1. We manually annotated the questions of our training set according to this taxonomy with both coarse classes and fine classes.

Result of experimentation

For the first experiments, the representation of the questions is simply accomplished by filtering the stop words by using a list of stop word http://www.lsi.upc.es/padro/lists.html.

In our approach, the words which are common and therefore not useful are filtered by using a list of 'stop words', modified to keep the words judged pertinent for our application (e.g., who, where are discriminating words in questions, and thus are not deleted). We applied the three learning algorithms. Their results are presented in Table 2 in the 'stop word' row.

In the second series of experiments, we used treetagger [START_REF] Schmid | TC project at the Institute for Computational Linguistics of the University of Stuttgart[END_REF] to obtain the part-of-speech tag, and then a filtering step using the list of stop words. The results are in the POS row of Table 2, and they show an improvement over the previous ones.

In the third series of experiments we used word N-grams. The results are presented in the last three rows of Table 2. For N = 1, we only consider unigram, and thus the method is the same as the simply filtering one 'stop word'. Moreover, the results obtained with N-grams with N greater than 4 were worse. This is why hereafter we will only refer to N-grams with N between 2 and 4. The best results are obtained with N = 2, and then the efficiency decreases as N increase. The best results are obtained with the SVM classifier.

With these experiments we have demonstrated that the use of either N-grams or part-of-speech tags or filtering improves the result. So, we then tried to combine those features. We successively applied treetagger, then filtering of stop words and N-grams with N ∈ {2, 4}.

Table 3 displays the results of the three classification learning algorithms on the same training set of questions. In general, we note that the results deteriorate when N = 3 or 4. The best results are obtained with N = 2 and with the SVM algorithm compared to K-NN and naive Bayes. The precision of classification improved from 68.2% to 73.5% with SVM and weighting with TF.IDF.

Discussion

Up until now, we have not used any semantics for classification. However, questions that should be classified in one category can also use different vocabulary either synonyms (e.g., birth and cradle) or hypernyms (e.g., city and town).

In what follows, we will present our approach based on a combination of the various features discussed in this section, and the expansion of the questions with hypernyms, synonyms, named entities for addressing the semantics of words.

Approach Sacseq

The aim of this section is to present the Sacseq approach (Cf. Figure 4). The general process is composed of four principal phases.

Phase 1 Corpus preprocessing

Label all the questions of the corpus according to the taxonomy. Thereafter, treetagger is used to annotate the words with part-of-speech tag, and their lemma. This information is relevant for the selection of a specific word category.

Phase 2 Question expansion 1 Projection and hypernym

Regarding the vocabulary diversity and the shortness of questions, many of semantically correlated words are treated as different (e.g., city and town are semantically correlated). We also try to expand questions with more general terms, as they unify the sense of the nouns. The notion of projection refers to a matching between a given word and the term representing a taxonomy concept.

The idea is to enrich the questions with synonyms or hypernyms of the nouns belonging to the question. For this purpose, we use WordNet. For each noun, the hypernym feature of WordNet provides a set of generic words at different levels, starting with the most specific and going to those who represent a broader meaning of the noun. While searching for hypernyms of noun words, we have to preserve the original semantics of the words. The different steps of 'projection and hypernym' expansion are the following:

• extract nouns from question

• for each noun, project on the 50 concepts of the taxonomy and their instances, if this noun belongs to an instance of a concept, the question will be expanded by this concept

• if it is identical to a concept, no changes are made • otherwise, for each remaining noun collect the set of hypernyms

• preserve the order assigned by wordNet to reflect the hypernym level of abstraction, then seek the first of these hypernyms that projects into the instances of our concepts or the concepts themselves.

Synonym expansion

This step proposes a new methodology to expand the questions with synomyms. Again, WordNet is the resource for finding synonyms of words. To maintain a semantic enrichment, we study the semantic correlation between a word and its set of synonyms. One of the most commonly used measures for finding how two words are correlated is cubic mutual information (MI) [START_REF] Downey | Locating complex named entities in web text[END_REF]. This measure depends on a context c. Given this context it is based on three frequencies: nb(x, c) the number of co-occurrences of x and c, nb(y, c) the number of co-occurrences of y and c, nb(x, y, c) the number of co-occurrences of x, y and c. The measure then is computed with ( )

3 3 (, ) (, ,) () () MI nb x y c AcroDef x y c nb x c nb y c ∧ = ∧ ⋅∧ (2)
We keep only the synonyms that were judged semantically close by the threshold of the highest similarity among the group of synonyms, then, we expand questions with the relevant synonyms.

To implement this measure, firstly we must identify the context c. We use a syntactic analyser (de Marneffe and Manning, 2008) to extract syntactical relations from the questions. Those relations define the (grammatical dependencies rules) among words of questions which are used later as the context of addressed words. To evaluate the three frequencies we post queries to Google. We then only retain synonyms for which the value of 2 is greater than a threshold, so that they are semantically correlated to the original term.

The following example illustrates the information available when applying the synonym expansion.

Question What is the capital of the French Republic?

The grammatical dependencies are: attr (is, what), det (capital, the), nsubj (is, capital), det (republic, the), amod (republic, French) and prep of (capital, republic).

After the parsing we detect that capital is the subject of the sentence. Based on the grammatical dependencies found (amod and prep_of), we find that French Republic is the context of capital. When collecting the set of synonyms of capital with WordNet we find: seat of government, city, principal, assets, and wealth. The original term capital in the context French Republic: The list above illustrates the 3

MI

AcroDef values for all these synonyms with the original term capital in the context French Republic. As we can see, regarding the context, the first two synonyms seat of government and city are the most appropriate and they have the largest values. Thus, we keep just these two synonyms to expand the question.

Named entities

After the two steps of question expansion by projection and hypernyms and synonyms, we use IdentFinder [START_REF] Bikel | Algorithm that learns what's in a name[END_REF] to assign a semantic category to some nouns in the questions. IdentFinder is able to tag 7 types of named entities person, description, location, profession, money, number and date.

Phase 3 Vectorisation

In this phase, first the questions of the corpus most be filtered using the list of stop words. Then, all the N-grams are extracted. Each N-gram is considered as a dimension of the vector space. Each question is then converted into a vector where the number of occurrences is weighted with TF-IDF.

Phase 4 Learning and classification

In this phase, 10-fold cross-validation is employed. Firstly, the classifier model is learned using the training corpus constituted of 90% of the corpus. Again, the three learning algorithms are SVM, KNN and NB. The classifier model is built by combining a sequence of two classifiers. The first classifies questions into the 6 coarse classes and the second into the 50 fine classes. Each uses the same learning algorithm. Then the classifier model is used to assign a class to each new question of the 10% rest of the corpus.

Algorithme of Sacseq. The principle of Algorithm 1 is as follows:

Algorithm 1 Sacseq

Input:

The learning Corpus of questions Q, Taxonomy T, WordNet, 3 ,

MI AcroDef

Threshold β

Output: Space vector V;

1 begin 2 for each q in Q do

3 q L = TreeTagger(q); 4 Q L = Q L ∪ q L ; 5 for each q L in Q do 6 S GD =
F LS t W L Q Filter Q - = 25
( ) 90%, ; F AL QP a r t Q = 26 for each q in Q A do 27 N -grammes(Q A ); 28 tf • idf (Q A ); 29 Vectorise(Q A ); 30 return V;
31 end

For each question, we apply TreeTagger for stemming and to get the grammatical category of the words. For all the nouns in each question of the new corpus, we use Project for project these nouns at the instance of the taxonomy. If the projection fails, we use Wordnet Hyp to search for hypernyms. Then, again we project the hypernym on instances of the taxonomy. In the step of synonyms, Wordnet Syn extract the synonym for each noun, then we calculate the correlation force between the noun and this set of synonyms using 3 MI AcroDef (s, Noun, S GD ), followed with Filtre(S s , β) to retain the relevant ones. At this step, we apply the filter to delete non relevant word using the list of stop words. The application of N-grams followed by TF-IDF will give us the space vector V, which will then be used as the training set to learn the algorithm.

Experiments

In this section, the results of the different experiments we conducted to validate our methodology are presented. We will particularly look at the following point:

• What are the consequences of the choice of the features on the quality of classification?

In the first experiments, classification is performed only with the integration of Projection and Hypernym, whose aim is to evaluate the improvement brought on by this method. We limit the calculation of frequencies to TF-IDF and we only use bi-grams.

Results are presented in Table 4. With the projection and hypernym method, we find that the percentage of correctly classified questions was improved with the three classification algorithms, and significantly with SVM which was improved by 7.4% (from 73.5% to 80.9% (Table 4 row projection and hypernym).

In the next experiments, we expanded questions with synonyms. Table 5 displays the classification results. The precision again is improved with the three learning algorithms, and especially with SVM which was improved by 5.1% (from 73.5% to 78.6%). The first two methods of expansion described above perform better than named entities. In the final series of experiments, we applied all the semantic steps of our approaches Sacseq. Table 7 displays the classification results. This demonstrates the usefulness of our expansion method and features combination. Precision is improved for all the learning algorithms, especially with SVM increasing by 13.2% from 73.5% to 86.7%. In this experiment, we want to know how many questions are required to produce a stable and robust training set. We thus applied the Sacseq method several times. Each time we have increased by 1,000 the number of question until we get a stability on the performance of classification. Figure 2 depicts the relationship between the size of the corpus and the percentage of classification. As we can notice, above 10,000 questions we do not increase much the percentage of classification. Future work may entail a broad series of projects and initiatives. Firstly, our method depends on the quality and the number of questions in the learning corpus. We would like to study the relationship between classification performance and the size of the learning corpus. Secondly, in this paper, we focused on machine learning. We plan to extend the first step of the classification by applying a set of hand written rules that cover the six coarse categories. Thirdly, we hope to extend this work to support interactive QA, where the users can interact with the system. Finally, we propose to complete this exploratory work within a complete QA system in the context of information retrieval in a corpus of structured documents.

  assets, French Republic) = 1.16 × 10 -4 4 3 MI AcroDef (capital, wealth, French Republic) = 1.0078 × 10 -principal, French Republic) = 3.097 × 10 -6

Figure 2

 2 Figure 2 Relation between the size of training corpus and the number of learned adjectives

Table 1

 1 Question classification taxonomy

	Coarse classes	Fine classes
	Abbreviation	Abbreviation, expression
	Description	Definition, description, manner, reason
	Entity	Animal, body, colour, creative, currency disease, event, food, instrument,
		lang letter, other, plant, product, religion, sport, substance, symbol, technique,
		term, vehicle, word
	Human	Description, group, individual, title
	Location	City, country, mountain, other, state
	Numeric	Code, count, date, distance, money order, other, period, percentage, speed,
		temp, volume size, weight

Table 2

 2 Features classification results

	Algorithms		K-NN	SVM		NB
	Weighting	Frq.	tf • idf	Frq.	tf • idf	Frq.	tf • idf
	Filtration	52.5	55.7	57	58.6	56.7	57.2
	Lemma	60.9	62.1	62,8	63.9	62.2	62.4
	2 grams	65.8	66.9	67.7	68.2	67.9	68.1
	3 grams	62.1	63.8	64.3	66.2	65	64.2
	4 grams	54.4	56.7	55.8	56	53.1	54.9
	Table 3	Combination classification results with lemmatisation, filtering, weighting and
		N-grams
	Algorithms		K-NN	SVM		NB
	Weighting	Frq.	tf • idf	Frq.	tf • idf	Frq.	tf • idf
	1 gram	60.9	62.1	62.8	63.9	62.2	62.4
	2 grams	71.3	71.2	72.5	73.5	71.9	72.3
	3 grams	64.7	66.3	65.9	66.7	65.3	65.7
	4 grams	55.9	57.1	56.7	57.2	56.3	56.6

Figure 1

The main process of Sacseq approaches (see online version for colours)

Table 4

 4 Classification results using projection and hypernym

	Algorithmes	K-NN	SVM	NB
	Projection and Hypernym	78.6	80.9	80.1

Table 5

 5 Classification results using synonymsTable6displays results when expanding questions by named entities. Again, the result with all algorithms is improved, especially with SVM by 3.1% (from 73.5% to 76.6%).

	Algorithmes	K-NN	SVM	NB
	Synonym	78.1	78.6	77.9

Table 6

 6 Classification results using named entity

	Algorithmes	K-NN	SVM	NB
	Named entity	76.5	76.6	76.3

Table 7

 7 Classification results using the Sacseq approaches Experiments related to training sets size vs. classification performance

	Algorithmes	K-NN	SVM	NB
	Sacseq	84.9	86.7	85.2


Yann Heuzé
email: heuze@cict.fr

Hugo F V Cardoso

Testing the quality of non-adult Bayesian dental age assessment methods to juvenile skeletal remains: the Lisbon collection children and secular trend effects

Keywords: dental development, age estimation, probabilistic methods, reference collection, socioeconomic status

Age estimation of non-adult skeletons from archaeological or forensic contexts has relied heavily on modern schedules of dental formation developed on samples of children of affluent populations. Although genetic factors have been considered to have had the greatest influence on population differences in dental development, increased interest has been placed on the role of environmental influences, such as differences in socioeconomic status and secular trends. This study evaluates the quality (i.e. accuracy and reliability) of two Bayesian dental age estimation methods to a sample of identified child skeletons from the Lisbon collection (20th century Portugal). The two Bayesian methods are developed on a reference sample of modern children from France, Ivory Coast, Iran and Morocco. The test sample from Lisbon, compared to the reference sample, is separated by over 50 years of secular trends and comprises a lower socioeconomic segment. The two Bayesian methods show that the Lisbon children are consistently one-year behind in dental age compared to the modern children of the reference sample. Environmental factors largely explain the differences between dental and chronological age in historic samples of non-adults.

Several methods for non-adult age estimation based on stages of tooth formation are available in the literature (e.g. [START_REF] Nolla | The development of the permanent teeth[END_REF]Moorrees et al., 1963a,b;[START_REF] Demirjian | A new system of dental age assessment[END_REF][START_REF] Gustafson | Age estimation up to 16 years of age based on dental development[END_REF][START_REF] Haavikko | Tooth formation age estimated on a few selected teeth. A simple method for clinical use[END_REF][START_REF] Anderson | Age of attainment of mineralization stages of the permanent dentition[END_REF]. However, the accuracy and reliability of most methods has seldom been examined on juvenile skeletal material. Some exceptions are the studies carried out by [START_REF] Saunders | Accuracy tests of tooth formation age estimations for human skeletal remains[END_REF] and [START_REF] Liversidge | Accuracy of age estimation from developing teeth of a population of known age (0-5.4 years)[END_REF][START_REF] Liversidge | Dental maturation of 18th and 19th century British children using Demirjian's method[END_REF]. One of the main difficulties in testing dental age estimation techniques comprehensively is that collections of identified juvenile skeletons are extremely rare. In addition, because some problems exist with radiographs of living children, particularly the very young and infants, these collections are particularly important for testing the quality of dental age assessment methods, although they too present some problems, namely in terms of sample size. Despite the fact that dental development is widely considered the single best indicator of chronological age at death in non-adult skeletal remains, it is very important to assess the accuracy of the methods in order for the researcher to decide the most reliable technique according to the material available and required level of accuracy. In addition, the testing of age estimation methods through utilization of diverse samples is fundamental to address the problem of uncertainty when a method is applied to an individual originating from a population that differs from the one that contributed to the development of the method.

Three difficulties are usually associated with the cross-population applicability of dental age methods: 1) biological differences between populations of specific geographic regions, due to different gene pools; 2) differences in living conditions and socioeconomic status between contemporaneous populations or positive secular changes in living conditions responsible for advancement in dental development in extemporaneous populations; 3) methodological issues. Several decades of research have identified population and regional differences in the timing of dental development [START_REF] Fanning | A comparison of permanent mandibular molar formation in Australian Aborigines and Caucasoids[END_REF][START_REF] Owsley | Formation of the permanent dentition in Arikara Indians: timing differences that affect dental age estimates[END_REF][START_REF] Nyström | Dental maturity in Finnish children, estimated from the development of seven permanent mandibular teeth[END_REF][START_REF] Harris | Tooth mineralization standards for blacks and whites from the middle southern United States[END_REF][START_REF] Mappes | An example of regional variation in the tempos of tooth mineralization and hand-wrist ossification[END_REF][START_REF] Tompkins | Human population variability in relative dental development[END_REF], thus providing support for population or geographic-specific methods, but recent research has shown that the quality of dental age assessment does not seem to depend predominantly on the use of geographic-specific standards [START_REF] Liversidge | Growth of permanent mandibular teeth of British children aged 4 to 9 years[END_REF][START_REF] Liversidge | Variation in modern human dental development[END_REF][START_REF] Heuzé | Chronologie et étiologie de la maturation macrostructurale des dents définitives[END_REF][START_REF] Braga | Non-adult dental age assessment: correspondence analysis and linear regression versus Bayesian predictions[END_REF][START_REF] Maber | Accuracy of age estimation of radiographic methods using developing teeth[END_REF][START_REF] Liversidge | Timing of Demirjian's tooth formation stages[END_REF]. In fact, there seems to be a marked degree of normal variation in the timing of dental development among different populations, and probably only a very small amount of it can be explained by genetic influences. Methodological factors have been identified as one potential source of variation in the detection of population and regional differences in the timing of dental development [START_REF] Harris | Tooth mineralization standards for blacks and whites from the middle southern United States[END_REF][START_REF] Simpson | A radiographic study of the development of the human mandibular dentition[END_REF]. However, unwarranted claims of resistance or insensitivity of dental development to environmental constraints due to high heritability [START_REF] Larsen | Bioarchaeology: interpreting behavior from the human skeleton[END_REF] have disregarded nutrition, disease, living conditions or secular trends as major influences in dental age estimates [START_REF] Holtgrave | Acceleration in dental development: fact or fiction?[END_REF][START_REF] Nadler | Earlier dental maturation: fact or fiction?[END_REF][START_REF] Cardoso | Patterns of growth and development of the human skeleton and dentition in relation to environmental quality: A biocultural analysis of a sample of 20 th century Portuguese subadult documented skeletons[END_REF][START_REF] Cardoso | Environmental effects on skeletal versus dental development: Using a documented subadult skeletal sample to test a basic assumption in human osteological research[END_REF] and, consequently, as important explanatory factors of population differences in dental development.

The purpose of this paper is to test the quality of two Bayesian methods of dental age estimation based on non-geographic-specific standards of the permanent dentition on a sample of 20th century non-adult documented skeletons from Portugal. A large sample of children from multiple geographic origins is used to develop the two Bayesian methods, which are subsequently applied to the identified series of non-adult skeletons. Our specific goals were to examine how a non-geographic-specific method would perform on a sample of non-adult skeletal remains and, given the results, what factors would better explain variation in dental age estimates, considering that the methods were developed on a contemporaneous sample of living children and the test case derives from an historic period, albeit recent, that differs in socioeconomic background.

MATERIALS AND METHODS

Reference sample

The reference sample consists of dental panoramic radiographs which were collected between 2001 and 2004, from 2,386 healthy children aged 1.9 to 16.0 years (1,346 girls and 1,040 boys) (Table 1). The sample has a broad age range and adequate sample sizes for all one-year age groups, except between the ages of 1.9 and 3.9 and older than 15.0, where only 62 and 65 children, respectively, are included in the sample. All children in the reference sample lived in the areas of Abidjan (Ivory Coast), Shiraz (Iran), Marrakech (Morocco) or in France (Bordeaux, Montpellier, Toulouse). The panoramic X-rays had been taken for diagnostic proposes and none of the children had undergone orthodontic treatment before taking the selected radiograph. No pathologic cases (i.e. for which a surgical operation was necessary) were selected. Only children who were free of anomalies in tooth numbers were selected. The children lived in environments where they experienced normal levels of infectious diseases and were not protected from environmental insults, corresponding to the definition of a reference sample [START_REF] Cameron | Methods of human growth research[END_REF], often called a training sample. The socioeconomic background of children living in France is mixed due to 1) the different places where the study was developed (i.e. hospitals and private clinics, representing a majority of lower and higher socioeconomic classes, respectively); 2) the fact that orthodontic treatments are free (repayment) in France thanks to social insurance (for more details on socioeconomic background of the sample from France see [START_REF] Heuzé | Chronologie et étiologie de la maturation macrostructurale des dents définitives[END_REF][START_REF] Heuzé | The impact of socioeconomic status in the estimation of non-adult dental age[END_REF]. Regarding the Ivorian, Iranian and Moroccan children, they largely represent the middle to high social class of their respective countries, mainly because orthodontic treatments are not free.

Therefore, the reference sample represents not only an ample spectrum of socioeconomic backgrounds from France, but also the affluent of the Ivorian, Iranian and Moroccan populations, which may not necessarily be at the same level of the French high socioeconomic segment, due to overall country-level differences in living conditions and socioeconomic development. Before the study was initiated it was ethically approved by a French institutional board (Commission Nationale de l'Informatique et des Libertés) and no regulations exist in Morocco, Iran or the Ivory Coast.

Test sample

The test sample is a 20th century cemetery sample and is derived from the Lisbon documented skeletal collection [START_REF] Cardoso | Brief communication: the collection of identified human skeletons housed at the Bocage Museum (National Museum of Natural History), Lisbon, Portugal[END_REF]. Because both the dependent and independent Bayesian methods tested here were deemed unreliable under the age of 4 and over the age of 15, due to small sample sizes in these age groups of the reference sample, only children between 4 and 15 years old were selected in the test sample. Consequently, the material from the Lisbon collection consists of the skeletal remains of 40 children between the ages of 4 and 15, of which 20 are females and 20 are males (Table 1). For all children age at death was calculated from the death and birth date, obtained from death and birth civil records. Children who showed inconsistencies between reported age at death in death records and age at death calculated by subtracting the date of death to the date of birth were also not selected. All children in the test sample were Portuguese-born and were buried in Lisbon between 1913 and 1972, but most (65%) died in the 1940s and 1950s. Most of the children represent the middle to low social class of the city of Lisbon, as inferred from the origin of the remains (temporary graves) and from the father's occupations, which include a large proportion of menial jobs [START_REF] Cardoso | Patterns of growth and development of the human skeleton and dentition in relation to environmental quality: A biocultural analysis of a sample of 20 th century Portuguese subadult documented skeletons[END_REF][START_REF] Cardoso | Environmental effects on skeletal versus dental development: Using a documented subadult skeletal sample to test a basic assumption in human osteological research[END_REF]. In addition, these children represent a population who was going through tremendous social and economic difficulties during Salazar's dictatorial regime between 1926 and 1974. Compared to the reference sample, the test sample is representative of a lower socioeconomic level, which is not only separated temporally from the other samples by several decades, but also by the improvements in living conditions that they entail.

Dental stage assessment method

The degree of formation of the crowns and roots for the seven permanent teeth of the mandible (I1 to M2) were assessed according to the stages defined by [START_REF] Demirjian | A new system of dental age assessment[END_REF].

Demirjian and co-workers defined eight stages of fractional development of the crown and root, assigned the letters A to H, which were converted to the numbers 1 to 8, respectively, in order to generate a dental mineralization sequence (DMS) for each individual. The DMS is the macrostructural event sequence observed on an individual's developing teeth at a precise moment of his life, i.e. it represents a formula with seven numbers that corresponds to the stages of development of each permanent tooth of that individual. For example, the DMS is equal to 88 8 87 87 if I1, I2, C, P3, P4, M1 and M2 are assessed as stages 8,8,8,8,7,8,7 respectively (or H, H, H, H, G, H, G in the original Demirjian's stages).

Assessment of tooth formation stages in the test sample was assessed by HC directly on loose teeth and on periapical radiographs and YH assessed tooth formation in the reference sample using panoramic X-rays. Intra-and inter-observer agreement was estimated in a random sample of 20 X-rays from the Lisbon collection, representing a total of 160 teeth.

Intra-observer agreement was always greater than 90% and inter-observer agreement was 74% (i.e. 118 out of 160 teeth were assessed with the same dental stage). In both intra-and inter-observer tests, when a difference existed, it was never greater than one stage. A signed Wilcoxon test also showed that the inter-observer difference in scores was equally likely to be positive or negative (T=59.5, p=0.6603), thus indicating that one observer is not systematically underscoring or overscoring relative to the other observer.

When dealing with human non-adult skeletal remains recovered from archaeological and forensic contexts, one is faced with the inability to accurately determine the sex of the individuals, due to the lack of reliable macroscopic methods for sex determination as most of the sex-specific traits are only developed during adolescence. Therefore, although this is an important limitation to anthropological studies, because sex-specific methods based on tooth formation can increase accuracy of age estimates, it is preferable to test the quality of the Bayesian method by pooling the sexes. In this way the test sample is treated as an archaeological or forensic sample of documented age and unknown sex, and non-sex specific standards were used for both dependent and independent Bayesian methods employed in this study.

Dependent Bayesian Method (DBM)

The principle of a Bayesian dental age assessment method (dependent or independent) is to produce for each individual, according to his/her dental formation status, a distribution of posterior probability of belonging to a particular age group. The age group with the highest posterior probability is the "dental age group" of the individual. In this study, one-year age intervals (12 months) were used to determine dental age groups, because they are closer to the required level of accuracy in archaeological samples. After having assessed stages of tooth formation, the dependent Bayesian method (DBM) using uniform priors [START_REF] Braga | Non-adult dental age assessment: correspondence analysis and linear regression versus Bayesian predictions[END_REF] was applied to each individual to estimate age by means of the DMS, since for each DMS there is a posterior probability distribution to be observed at different age groups. The particularity of DBM is that, by using the DMS, it considers the seven permanent mandibular teeth as dependent attributes. In fact, the DMS is the result of a dynamic pattern corresponding to sequenced, interrelated mechanisms and processes between developing teeth. A limited variability (but not necessary a low variability) in DMS is observed because teeth are topographically, developmentally and functionally associated to each other, and essentially grow as a unit [START_REF] Heuzé | Chronologie et étiologie de la maturation macrostructurale des dents définitives[END_REF][START_REF] Braga | Non-adult dental age assessment: correspondence analysis and linear regression versus Bayesian predictions[END_REF]. The inconvenience of DBM concerns the age assessment of children who have a DMS not represented in the reference sample. Because of mathematical specificities of DBM, the dental age of these children cannot be assessed (for more details see [START_REF] Braga | Non-adult dental age assessment: correspondence analysis and linear regression versus Bayesian predictions[END_REF]. It is important to note, however, that DBM is able to assess dental age of incomplete (i.e. by examining just 1, 2, 3, 4, 5 or 6 permanent mandibular teeth) and of complete dentitions (i.e. all 7 permanent mandibular teeth).

Independent Bayesian Method (IBM)

Developing teeth can also be studied as independent attributes. Although this does not correspond to the biological reality of the development process, some researchers have developed an independent Bayesian method (IBM) for dental age assessment associated with either non-uniform priors [START_REF] Lucy | A Bayesian approach to adult human age estimation from dental observations by Johanson's age changes[END_REF][START_REF] Chaillet | Applications anthropologiques de l'approche Bayésienne dans la détermination de l'âge des immatures[END_REF][START_REF] Foti | New forensic approach to age determination in children based on tooth eruption[END_REF] or with uniform priors [START_REF] Heuzé | Chronologie et étiologie de la maturation macrostructurale des dents définitives[END_REF]. Only the uniform priors approach is used in this paper. Compared to DBM, IBM offers the possibility to generate dental age estimations for more children than DBM, because calculations are made "tooth by tooth" and not "DMS by DMS", as illustrated by the following example. Using a hypothetic sample of three children A, B, and C with "I1 and I2" at stage "8 and 7", "8 and 8", and "7 and 6", respectively, the probability to present "I1 and I2" at stage "8 and 7" is computed as "2/3 x 1/3" with IBM, because stage "8" is represented by two children and stage "7" by one child. The probability to present "I1 and I2" at stage "8 and 7" is computed as "1/3" with DBM, because there is only one child with "I1 and I2" at stage "8 and 7"; the individual A. Because the probability of finding the same tooth at the same stage of dental development in both the reference and test sample is always greater or equal to the probability of finding the same DMS in both the reference and test sample (for more details on calculations see [START_REF] Lucy | A Bayesian approach to adult human age estimation from dental observations by Johanson's age changes[END_REF][START_REF] Braga | Non-adult dental age assessment: correspondence analysis and linear regression versus Bayesian predictions[END_REF], the ability to assess the age of an individual is increased by using IBM rather than using DBM. On the other hand, dental age cannot be assessed on an individual whose stages of development of the seven teeth are not represented in at least one age group of the reference sample. Contrary to DBM, the dental stages of the test individual can be represented by different individuals in the same age group of the reference sample. In our hypothetic sample, assume A, B, and C represent three individuals of the reference sample in the same age group; IBM will be able to produce a dental age for a test individual with "I1 and I2" at stage "8 and 6", but DBM will not because the DMS "8 and 6" is not represented in the hypothetic reference sample. Like DBM, IBM is able to assess dental age in incomplete dentitions according to only 1, 2, 3, 4, 5, or 6 permanent mandibular teeth and also in complete dentitions (i.e. all 7 permanent mandibular teeth). dental age is three one-year groups behind true chronological age then the child is assigned a rank of -3.

Assessing the quality of dental age assessments

The quality of the dental age assessments were obtained by calculating four parameters: 1) percentage of response; 2) 95% credible interval; 3) performance; and 4) symmetry to rank 0. Percentage of response corresponds to the number of children in the sample who could be assigned a dental age. When using the DBM, the percentage of response indicates the number of children who could be assigned a dental age by comparing his/her DMS with those of the reference sample. In contrast, when using the IBM, the percentage of response corresponds to the number of children who could be assigned a dental age by comparing each individual's tooth stage with those of the reference sample. The Bayesian 95% credible interval is a posterior probability interval and provides a measure of reliability (in months) of the dental method. It is determined by choosing the interval of ranks (number of one-year intervals), centered on rank 0 and containing 95% of the individuals in the test sample. The Bayesian 95% credible interval is analogous to the more common 95% confidence interval used in frequentist statistics. For example, if to include 95% of the individuals in the test sample we establish a rank interval from -3 to +3, the credible interval of the method will be 7×12 months=84 months, with 7 being the number of ranks in the interval (3 ranks below zero + 1 rank zero + 3 ranks above zero) and 12 months the one-year interval of each rank. Thus, the posterior probability that any individual lies in the interval from -3 to +3 is 0.95. Performance corresponds to the percentage of children classified in rank 0, i.e. the percentage of children whose age was estimated with the best accuracy (±6 months).

The symmetry to rank 0 allowed the authors to study the relative proportions of both positive and negative ranks and, thus, provides a measure of relative advancement or delay in dental ages, respectively. A statistically significant majority of negative ranks is represented by a minus sign (-), and a statistically significant majority of positive ranks by a plus sign (+).

These four quality parameters (percentage of response, 95% credible interval, performance, and rank distribution symmetry to rank 0) were calculated for each method (DBM and IBM) and for each sample, the reference and the Lisbon (test) samples.

Crossvalidation [START_REF] Tukey | Exploratory data analysis[END_REF] was the method used to obtain the quality parameters of the reference sample using both DBM and IBM. The results for each method and sample were then contrasted and compared. The reference sample results comprise the model of "optimal quality" against which the quality of the test sample is compared. Chi-square tests were used to test whether the rank distributions differed between the reference and test samples. Distribution of ranks in the test sample were considered the observed frequencies and distribution of ranks in the reference sample were used as the expected frequencies. Although there are no specific recommendations for how small a sample can be to be suitable for a chi-square test, the general rule of thumb is that the smallest expected frequency should be five or more [START_REF] Sokal | Biometry: the principles and practice of statistics in biological research[END_REF]. Therefore, whenever rank classes with expected frequencies of less than five occurred, expected and observed frequencies for those classes were pooled with an adjacent class to obtain a joint class with an expected frequency greater than five. In order to be sure that the age structure of the reference sample and of the test sample is not influencing the results due to older children tending to be more delayed than younger children (they may accumulate more growth deficit over the years), the two were also compared using a chi-square test. All comparisons were guided by a 5% significance level. All Bayesian calculations were performed using a Microsoft Excel 2000® Visual Basic macro created by Dr. Houët (from UMR 5199 PACEA, University of Bordeaux 1, France). This Microsoft Excel 2000® Visual Basic macro has been used in previous studies [START_REF] Heuzé | Chronologie et étiologie de la maturation macrostructurale des dents définitives[END_REF]Braga et al., 2005) and is available upon request to YH.

RESULTS

The age distributions of both the reference and test samples are shown in Table 1 and do not show any significant differences (χ²=0.42, p>0.99, df=10). Quality parameters of age estimation in both the reference and test samples are presented in Table 2. The percentage of response for both samples and both methods are similar, although only the reference sample shows 100% of response using IBM. With respect to the 95% credible interval, both samples do not differ when using the two methods, showing an interval of 84 months. In other words, the percentage of individuals with ranks comprised between -3 and +3 (84 months) allowed us to combine at least 95% of the tested sample. The Lisbon sample shows a lower performance in both methods compared to the reference sample, which means fewer individuals at rank 0. This is related to the fact that whatever the method used, the Lisbon sample presents a significant and consistent majority of negative ranks (i.e. delay in dental age) and the mode of both rank distributions obtained with the Lisbon sample are shifted to the negative rank values. These significant asymmetries to rank 0 of the test sample contrast with the corresponding rank distribution obtained with the reference sample, where with DBM a significant majority of positive ranks is observed (i.e. advance in dental age) and with IBM no significant asymmetry exists.

When DBM is used, the distribution of ranks obtained with the test sample was compared to the distribution of ranks obtained with the reference sample and is illustrated in Figure 1. The same comparison was carried out when IBM is used and is shown in Figure 2.

Statistically, the distribution of ranks obtained with the test sample always differed significantly from the distribution of ranks obtained with the reference sample in either the dependent (χ²=19.71, p<0.01, df=4) and independent Bayesian methods (χ²=33.25, p<0.01, df=4). Data in both graphs show that the Lisbon children are consistently and systematically one-year delayed relative to the reference sample children.

DISCUSSION

Results in this study show that both dependent and independent Bayesian methods were relatively precise in determining the age of the Lisbon children, but were not accurate. This means that, in the test sample, both Bayesian methods provided consistent results in relation to each other, showing similar percentages of response (IBM slightly higher), equal 95% credible intervals and similar performances and symmetries to rank 0. However, when the test sample results are compared to the reference sample results, the Lisbon children show a one-year delay relative to the reference sample children. As a result, the test sample shows considerably lower performances and a majority of negative ranks in both dependent and independent Bayesian methods compared to the reference sample. This delay cannot be interpreted as a methodological bias, since the validation of the reference sample (using cross validation) did not show any significant majority of negative ranks (i.e. delay in dental age).

On the contrary, the validation step showed either a significant majority of positive ranks with DBM (i.e. advance in dental age) or no asymmetry in ranks using IBM. In addition, the rank distributions for both test and reference samples are statistically different and are displaced by one rank (one year) thus providing further support for a consistent delay in dental development between the children in the test sample and in the reference sample. Since both reference and Lisbon samples did not present any significant difference in age distributions, this delay cannot be the consequence of differing age distributions. Although the power to find a difference in age distributions of the two samples may be considered low given the small test sample size; the chi-square statistic is a robust test [START_REF] Zar | Biostatistical analysis[END_REF] and only the power to detect very small differences is likely to be affected.

The similarity of results between DBM and IBM in the test sample was also observed in the quality parameters of the reference sample, with the exception of the symmetry to rank 0. Therefore, DBM and IBM provided basically the same results and this could mean the individual teeth provide enough accuracy and that the relationship between teeth does not add to the prediction of the dental age. However, in the reference sample, DBM results showed a majority of positive ranks (i.e. advance in dental agesee Table 2) and, given that the reference sample includes a significant majority of females, this advancement may suggest a greater sensitivity of this method to sex differences in dental development. Several studies have reported sex differences in both permanent teeth emergence [START_REF] Vo | Ranges of normalcy in the eruption of the permanent teeth[END_REF][START_REF] Dahlberg | Emergence of the permanent teeth in Pima Indian children[END_REF][START_REF] Garn | Variability of tooth formation[END_REF] were the firstsee [START_REF] Demirjian | Dentition[END_REF] for more details) and formation; females reaching most stages ahead of males [START_REF] Haavikko | The formation and alveolar and clinical eruption of the permanent teeth, an orthopantomograph study[END_REF] reported difference between 0.3 and 1.7 years). A recent study on the chronology of dental macrostructural mineralization using DBM and 6-month age groups confirmed these sex differences [START_REF] Heuzé | Chronologie et étiologie de la maturation macrostructurale des dents définitives[END_REF].

The inability of dental age estimation methods, based on several teeth, to assess relative heterochrony in dental development (i.e. patterning) is one important problem with both Bayesian methods; they both depend exclusively on the timing information (as the majority of subadults dental age assessment methods) of individual teeth that can be estimated by the mean of dental stages. Because the timing information is dependent on the number of teeth from which the mean of dental stages is calculated, it is important to quantify the influence over the dental age estimation quality of the number of teeth available. However, in a recent study applying both dependent and independent Bayesian methods to assess the dental age of the Spitalfields collection children, [START_REF] Heuzé | Application of non-adult Bayesian dental age assessment methods to skeletal remains: the Spitalfields collection[END_REF] showed that the quality of both Bayesian methods remains relatively stable regardless of the number of teeth available in each individual. The authors also pointed out that the teeth that complete their development later (i.e. mainly P4, M2 and secondly P3 and C) are more "powerful" (i.e. more useful) in age assessments than teeth that complete their development earlier.

Another problem related to patterning is the fact that dental age cannot be assessed with DBM on an individual whose DMS is not represented in the reference sample, or with IBM, on individuals whose stages of development of the available teeth are not represented at least in one age group of the reference sample. In the test sample, only one child could not be aged using IBM and DBM (specimen# 1448; DMS 55 4 31 53) and three other children could not be aged using DBM. This caveat of the methods is important because there may be a systematic bias in particular teeth and stages which are not being incorporated into the Bayesian estimate. However, such bias could only explain the inability to determine the age of just one child (specimen# 1448), since in the other three, failure to assess dental age is a result of the relative heterochrony between the stages of mineralization of the different teeth compared to the reference sample. For example, on the first child (specimen# 385; DMS 65 4 35 64), P4 shows a relative advance to C and especially to P3. The second child (specimen# 1561; DMS 65 5 5_ 74) shows a relative advance of M1. On the third child (specimen# 1584; DMS 88 6 87 86), C shows a relative delay and P4 a relative advance. Interestingly, all four children are boys.

A fairly clear amount of variation can be seen in most reference samples utilized by osteologists and the magnitude of such variation is rarely incorporated into studies (exceptions include [START_REF] Hoppa | Evaluating human skeletal growth: An Anglo-Saxon example[END_REF]. The Bayesian approach used in this study should account for the variation of development time for individual teeth and their stages and for variation that results from random fluctuations in the teeth present for analysis (the relative concordance in dental ages between teeth) and from using combined sexes tooth timings, that could explain what appears to be accelerated or delayed development. Therefore, although environmental effects have not been considered important factors as sources of variation in dental age assessments, the authors believe that the differences in dental development between the reference and Lisbon samples can be ascribed to socioeconomic differences that separate both samples. These differences reflect not only absolute social and economic conditions in populations of both samples, but also secular trends. The reference sample is comprised of modern children, whereas the test sample is comprised of early 20th century deceased children. Therefore, both samples are separated by several decades of history, that reflect social, economical and political transformations in each society, resulting in changes towards better nutrition, especially more protein and caloric intake during infancy, greater overall sanitary conditions and hygiene, lessening of disease as well as delivery of social and medical care. All these improvements are known to modify growth and development by accelerating physical maturation of children over time [START_REF] Susanne | Living conditions and secular trend[END_REF][START_REF] Tanner | Fetus into man: physical growth from conception to maturity[END_REF][START_REF] Malina | Research on secular trends in auxology[END_REF][START_REF] Bogin | Patterns of human growth[END_REF]. Even if the reference sample children from Ivory Coast, Iran and Morocco represent populations who have not yet experienced significant secular changes, compared to the reference sample children from France, they do represent the high to middle social class of their respective countries, and all the benefits, in terms of access to adequate nutrition and to health care, that it entails. Similarly, although the French segment of the sample comprises low socioeconomic status children, they are only 10.3% of the sample [START_REF] Heuzé | Chronologie et étiologie de la maturation macrostructurale des dents définitives[END_REF] and represent an affluent population who had already experienced major secular changes, including achievements in medical care. Therefore, it is likely that children in the reference sample show accelerated dental maturity compared to the Lisbon children. In fact, the last 50 years have witnessed notable improvements in living conditions of European populations, and those secular changes may explain the acceleration in dental formation that has been detected in 3-to 9-year-old European boys between 1960 and 1997 [START_REF] Holtgrave | Acceleration in dental development: fact or fiction?[END_REF], and in 8.5-to 14.5-year-old boys and girls in the US, between the 1970s and the 1990s [START_REF] Nadler | Earlier dental maturation: fact or fiction?[END_REF]. In addition, inability to determine age using DBM, due to a certain DMS not being represented in the reference sample, suggests that socioeconomic status, living conditions, or secular trends could affect not only dental age, but also relative dental development (i.e. patterning).

In contrast to the reference sample children, the Lisbon children experienced poor living conditions and limited access to proper nutrition and health care, which affected their developmental and growth status [START_REF] Cardoso | Patterns of growth and development of the human skeleton and dentition in relation to environmental quality: A biocultural analysis of a sample of 20 th century Portuguese subadult documented skeletons[END_REF][START_REF] Cardoso | Environmental effects on skeletal versus dental development: Using a documented subadult skeletal sample to test a basic assumption in human osteological research[END_REF]. However, applying a modified version of the Moorrees et al.'s (1963a,b) dental aging method using Demirjian et al.'s (1973) dental stages, [START_REF] Cardoso | Patterns of growth and development of the human skeleton and dentition in relation to environmental quality: A biocultural analysis of a sample of 20 th century Portuguese subadult documented skeletons[END_REF][START_REF] Cardoso | Environmental effects on skeletal versus dental development: Using a documented subadult skeletal sample to test a basic assumption in human osteological research[END_REF] reported a non-significant delay in dental development of Lisbon children (individuals aged 0 to 12 years) of low socioeconomic status compared to high socioeconomic status. Overall, dental age of Lisbon children was also not significantly delayed to chronological age [START_REF] Cardoso | Patterns of growth and development of the human skeleton and dentition in relation to environmental quality: A biocultural analysis of a sample of 20 th century Portuguese subadult documented skeletons[END_REF][START_REF] Cardoso | Environmental effects on skeletal versus dental development: Using a documented subadult skeletal sample to test a basic assumption in human osteological research[END_REF] and this contradicts the results in this study. Results with both Bayesian methods show a dental delay in Lisbon children which does not seem to derive from methodological bias. Consequently, it seems that the modified Moorrees et al.'s aging method may be overestimating dental age in the Lisbon children. In fact, research carried out by Simpson and Kunos (1999) suggests that the standards of Moorrees et al. may overestimate chronological age. Several studies [START_REF] Hägg | Dental maturity as an indicator of chronological age, the accuracy and precision of three methods[END_REF][START_REF] Poyry | Comparison of two tooth formation rating methods[END_REF][START_REF] Staaf | Age estimation based on tooth development, a test of reliability and validity[END_REF][START_REF] Mörnstad | The validity of four methods of age determination by teeth in Swedish children[END_REF][START_REF] Koshy | Dental age assessment: the applicability of Demirjian's method to South Indian Children[END_REF][START_REF] Nykänen | Validity of the Demirjian method for dental age estimation when applied to Norwegian children[END_REF][START_REF] Liversidge | Dental maturation in British children: are Demirjian's standards applicable?[END_REF][START_REF] Willems | Dental age estimation in Belgian children: Demirjian's technique revisited[END_REF][START_REF] Eid | Assessment of dental maturity of Brazilian children aged 6 to 14 years using Demirjian's method[END_REF]Hedge and Sood, 2002) using different samples (age structures, "geographic origins") reported that Demirjian's method [START_REF] Demirjian | A new system of dental age assessment[END_REF][START_REF] Demirjian | New systems for dental maturity based on seven and four teeth[END_REF], another widely used aging method for subadults, overestimated chronological age, thus providing dental ages that are advanced relative to chronological age. Applying the Demirjian's method [START_REF] Demirjian | A new system of dental age assessment[END_REF][START_REF] Demirjian | New systems for dental maturity based on seven and four teeth[END_REF] to the identified juvenile skeletons of the Spitalfields collection (18th and 19th centuries), [START_REF] Liversidge | Dental maturation of 18th and 19th century British children using Demirjian's method[END_REF] reported non-significant differences between dental age and chronological age and suggested modern dental formation schedules for Spitalfields children. These children were the sons and daughters of middle-to upper-class members of the Huguenot congregation buried in the Spitalfields church crypt [START_REF] Cox | Life and death in Spitalfields 1700 to 1850[END_REF]. However, regardless of the relative wealth of families, these children did not necessarily receive the best care and the industrial environment of London (overcrowding, air pollution, and inadequate sewage disposal) contributed significantly to deaths in early childhood and to growth retardation, exacerbated by the high prevalence of rickets and scurry [START_REF] Lewis | Impact of industrialization: comparative study of child health in four sites from medieval and post medieval England (A.D. 850-1859)[END_REF]. In addition, not only were these middle to high socioeconomic children not buffered from environmental insults, but they were also living at a time which had not benefited from recent improvements in sanitation, medical care and food preparation. We can reasonably conclude, therefore, that this lack of significance between dental and chronological age in the Spitalfields children [START_REF] Liversidge | Dental maturation of 18th and 19th century British children using Demirjian's method[END_REF] is due to the tendency of the Demirjian's method [START_REF] Demirjian | A new system of dental age assessment[END_REF][START_REF] Demirjian | New systems for dental maturity based on seven and four teeth[END_REF] to overestimate dental age (as the modified Moorrees et al's method) and does not represent the biological reality of the sample. The fact that the Spitalfields children were not found to be dentally delayed relative to the more modern Demirjain standards, also seems contrary to the findings of [START_REF] Holtgrave | Acceleration in dental development: fact or fiction?[END_REF] and [START_REF] Nadler | Earlier dental maturation: fact or fiction?[END_REF], who showed an acceleration in dental maturity during the past 40 years as a consequence of secular trends. Although, at first hand, the socioeconomic status of the Spitalfields children seems quite different to that of the Lisbon children, they tend to share several features. They are both comprised of deceased children who were growing up in poor environments, prior to the era of antibiotics and of other achievements in health care.

Additional evidence for the influence of environmental factors in dental development can be found by comparing the amount of overestimation in chronological age in the several studies that used Demirjian's method [START_REF] Demirjian | A new system of dental age assessment[END_REF][START_REF] Demirjian | New systems for dental maturity based on seven and four teeth[END_REF].

Overestimation seems least in samples of industrialized nations and greatest in samples of developing countries. For example, while in Indian children overestimation amounted to 3.04 years for boys and 2.82 for girls [START_REF] Koshy | Dental age assessment: the applicability of Demirjian's method to South Indian Children[END_REF], it only amounted to 0.14 and 0.04 years for Belgian boys and girls, respectively (Hedge and Sood, 2002). It is also interesting to note that British children of different geographic origins, but who grew up in the UK, show similar amounts of overestimation when Demirjian's standards are applied [START_REF] Liversidge | Dental maturation in British children: are Demirjian's standards applicable?[END_REF]. This suggests that any non-methodological influences on dental age estimation must be due to overall shared socioeconomic status and living conditions that affect nutrition and health care that, in turn, impact on dental development.

Using different aging methods (Moorrees et al., 1963a,b;[START_REF] Demirjian | A new system of dental age assessment[END_REF][START_REF] Demirjian | New systems for dental maturity based on seven and four teeth[END_REF] to estimate dental age of identified skeletal collections, some authors [START_REF] Saunders | Accuracy tests of tooth formation age estimations for human skeletal remains[END_REF][START_REF] Liversidge | Dental maturation of 18th and 19th century British children using Demirjian's method[END_REF][START_REF] Cardoso | Environmental effects on skeletal versus dental development: Using a documented subadult skeletal sample to test a basic assumption in human osteological research[END_REF] reported non-significant differences between dental and chronological ages in non-adult skeletal remains. This seemed to justify the assertion that these dental aging methods were suitable for age assessment of historical and archaeological non-adult skeletal remains. Although problems with the standards of Demirjian et al. and Moorrees et al. may be methodological, results in this study archaeological or written sources to infer the population's living standards. This issue may also affect forensic applications, particularly if the remains that need to be identified belong to a child of lower socioeconomic status in an under-developed country and the reference standard used to estimate dental age has been developed on the affluent segment of more developed nations. Moreover, more attention has to be given to the potential influence of socioeconomic status, living conditions and secular trends over relative dental development and dental sequences.

Fig. 1 .

 1 Fig. 1. Distribution of ranks in the test sample compared to the distribution of ranks in the

Fig. 2 .

 2 Fig. 2. Distribution of ranks in the test sample compared to the distribution of ranks in the

  Each child was assigned to one-chronological-year age group (e.g. if the child is 6.4 years old, the chronological age group is [6-7[). For each individual assessed, the dental age group (the age interval with the highest posterior probability) was compared to the chronological age group and subsequently given a rank (dental age group minus chronological age group). If the child's dental age group overlaps the chronological age group, he or she was given a rank 0. If the rank value is positive, dental age is advanced relative to chronological age, and if it is negative, dental age is delayed. The absolute value of the rank indicates how many age groups the dental age differs from chronological age. For example, if

ACKNOWLEDGEMENTS

The authors would like to thank the anonymous reviewers for their helpful comments and Sandra Albanese for editorial suggestions.

Grant Sponsor: Yann Heuzé was funded by the Foundation Fyssen. Hugo FV Cardoso was funded by Fundação para a Ciência e Tecnologia, Portugal (grant# SFRH/BD/4917/2001 and SFRH/BPD/22142/2005).

show that the application of modern probabilistic dental age methods [START_REF] Heuzé | Chronologie et étiologie de la maturation macrostructurale des dents définitives[END_REF]Braga et al., 2005) to archaeological samples can be problematic, due to population differences in socioeconomic status and in living conditions, and to secular trends. When one is dealing with children who experienced poor living conditions, it is likely that delays in dental development will determine a lower accuracy for dental age estimations. Although the children in the test sample do not represent either the affluent or the extremely disadvantaged segments of the 20th century Lisbon society [START_REF] Cardoso | Patterns of growth and development of the human skeleton and dentition in relation to environmental quality: A biocultural analysis of a sample of 20 th century Portuguese subadult documented skeletons[END_REF][START_REF] Cardoso | Environmental effects on skeletal versus dental development: Using a documented subadult skeletal sample to test a basic assumption in human osteological research[END_REF], they may serve as a reference sample for many ecologically diverse populations prior to the antibiotic era. It is not implied that this population is representative of prehistoric or historic populations, but it can provide an important test for examining the factors that influence the interpretation of developmental patterns in skeletal samples.

CONCLUSION

The two main purposes of this study were to test two Bayesian dental aging methods (with dependent or independent assumptions) in a large identified skeletal collection, and to interpret the origin of the potential discrepancies between the chronological and dental ages in the test sample. The subadults of the Lisbon collection provided an appealing opportunity to test those methods and examine their overall accuracy. Our results showed a general tendency of the Lisbon children to be consistently and systematically one-year delayed relative to the reference sample, regardless of the method utilized. This suggests that skeletal biologists should be very careful when determining the age of non-adult skeletal remains. Dental age may be the best indicator of chronological age but differences between populations may occur due to differences in living conditions, overall socioeconomic status or to secular trends that affect the accuracy of the dental age estimates. This is particularly true for archaeological studies, where older material is being examined and less information can be gathered from 2 Significance level of the difference between positive and negative rank proportions (symmetry to rank 0). Majority of negative ranks is shown as (-), majority of positive ranks as (+).


Jérémy Bourgalais
email: jeremy.bourgalais@latmos.ipsl.fr

Nathalie Carrasco

Main ions in the

HAL is

Introduction

Thermospheres of exoplanets are photochemically active layers, characterized by an efficient photolysis of the main components of the atmospheres. Vertical transport in thermospheres is moreover governed by molecular diffusion, also contributing to strongly modify the composition profiles of the atmospheres. On Mars, with an atmosphere based on CO 2 and N 2 , the efficient photolysis of CO 2 leads to an increase of CO mixing ratio, up to several tens percent's compared to CO 2 [1]. The impact on the thermal profile of the atmosphere is determining. On Mars the progressive enrichment in CO compared to CO 2 according to altitude limits the heating of the thermosphere, as CO is a less efficient UV absorber than CO 2 [2]. Predicting and understanding the temperature and density profiles of thermospheres of exoplanets will therefore constrain atmospheric escape and photoevaporation processes, and a fortiori the evolution of atmospheres of exoplanets.

Photolysis in thermospheres involves harsh UV and X-ray stellar radiations and produces complex chemical environments coupling neutral and ion chemistry. Ion-chemistry has been shown to be largely underestimated and poorly known when the Cassini-Huygens space mission unveiled the complex ion and neutral composition of the thermosphere of the largest satellite of Saturn, Titan [3]. Its atmosphere is based on N 2 and CH 4 , and nitrogen chemistry was found to be particularly important in Titan's thermosphere. We learned with the study of this body that ion-neutral chemistry was rich and efficient and could lead to unexpected abundant chemical species.

With the data of the California-Kepler Survey two populations of super-Earths and mini-Neptunes could be distinguished [4]. Super-Earths, with radii lower than 1.5 R ⊕ are rocky planets with thin atmospheres mainly made of heavy molecules like N 2 and CO 2 . Mini-Neptunes with masses between 2 and 3 R ⊕ have on the opposite extended H 2 -based atmospheres.

The aim of the present work is to characterize the main positive ions that can be expected in the thermospheres of super-Earths and mini-Neptunes. For this purpose we simulated experimentally the ion-neutral chemistry initiated by Far-UV radiations on a gas mixtures mimicking the main possible composition of thermospheres of super-Earths and mini-Neptune. The ion species are analyzed in situ by mass spectrometry.

Methods

Far-UV photons mimicking the stellar UV field were generated by using a gas-discharge type Far-UV source coupled windowless to our photochemical reactor [5]. We irradiated at 73.6 nm (15.6 eV by using the resonant emission lines of Ne I and Ar I, respectively, with a photon flux of ca. 1-5x10 14 ph.s -1 .cm -2 .

Gas mixtures were chosen to be representative of H 2poor atmospheres and H 2 -rich atmospheres. As the photolysis of CO 2 mainly produces CO, and that CO is more efficient to drive further photochemistry, we have chosen CO as a proxy of both CO 2 and CO in our experiments. In order to build a consistent experimental series, we have chosen to only modify the H 2 content in our experimental conditions. N 2 mixing ratio was therefore arbitrary chosen as equal to CO mixing ratio, and H 2 mixing ratios increased from 1% up to 96%.

The gas composition was monitored in steady state by using a high sensitivity (<1ppm) quadrupole mass spectrometer (Hiden Analytical EQP 200 QMS) allowing in situ measurements of the positive ions.

Results

H 2 mixing ratios were chosen at 1%, 33% and 96%. The main ions detected are shown on Figure 1. The first striking result is that in all conditions the main ions are the same: H 3 O + at m/z 19 and HCO + and N 2 H + at m/z 29, even in a H 2 -based neutral gas mixture. In the H 2 -based condition (H 2 mixing ratio of 96%), H 3 + at m/z 3 appears as an additional important ion contributor.

Figure 1: Ions produced after irradiation at 73 nm of H 2 /CO/N 2 gas mixtures. H 2 mixing ratios was chosen at 1%, 33% and 96%.

Primary ions produced by photoionization at 73nm are respectively H 2 + at m/z 2, N 2 + and CO + at m/z 28. Those ions react with H 2 , through ionmolecule efficient reactions, leading to the stable protonated ions observed. The detection of the ion H 3 O + is a sensitive probe of the presence of H 2 O in the reactive medium: as a photoproduct and/or as contaminant.

Summary and Conclusions

We highlight that the main ions observed in our H 2 rich (96%) and H 2 poor (1%) conditions are similar and corresponds to HCO + and N 2 H + . We used CO as a proxy for CO and CO 2 . We can extrapolate that HCO 2 + would similarly be observed in the presence of CO 2 . Despite the drastic differences in neutral compositions of the atmospheres of super-Earths and mini-Neptunes, our work suggests that rather similar ion contributions could be expected in their thermospheres.

Acknowledgements

This research was supported by the ERC Starting Grant PRIMCHEM, grant agreement n°636829.