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  'apport de l'expérimentation archéologique pour la compréhension de l'architecture carolingienne à poteau planté : les exemples du chantier d'Orville (Val-d'Oise) Frédéric Epaud, François Gentili To cite this version: Frédéric Epaud, François Gentili. L'apport de l'expérimentation archéologique pour la compréhension de l'architecture carolingienne à poteau planté : les exemples du chantier d'Orville (Val-d'Oise). Revue archéologique de Picardie, 2009, 1/2, pp.129-144. hal-01819410


Manel Zoghlami
email: manel.zoghlami@gmail.com.

Sabeur Aridhi

Mondher Maddouri

Engelbert Mephu Nguifo

AN OVERVIEW OF in Silico METHODS FOR THE PREDICTION OF IONIZING RADIATION RESISTANCE IN BACTERIA

Keywords: bacterial ionizing radiation resistance, multiple instance learning, phenotype prediction

Ionizing-radiation-resistant bacteria (IRRB) could be used for bioremediation of radioactive wastes and in the therapeutic industry. Limited computational works are available for the prediction of bacterial ionizing radiation resistance (IRR). In this chapter, we present some works that study the causes of the high resistance of IRRB to ionizing radiation. Then we focus on presenting in silico approaches that use protein sequences of bacteria in order to predict if an unknown bacterium belongs to IRRB or ionizing-radiation-sensitive bacteria (IRSB). These approaches formulate the problem of predicting bacterial IRR as a multiple instance learning (MIL) problem where bacteria represent the bags and

Introduction

IRRB could be used for the treatment of mixed radioactive wastes by developing a strain to detoxify both mercury and toluene [START_REF] Brim | Engineering Deinococcus radiodurans for metal remediation in radioactive mixed waste environments[END_REF]. These organisms are also being engineered for in situ bioremediation of radioactive wastes [START_REF] Brim | Engineering Deinococcus geothermalis for bioremediation of hightemperature radioactive waste environments[END_REF]. In [START_REF] Gabani | Radiation-resistant extremophiles and their potential in biotechnology and therapeutics[END_REF], the authors discuss the potential uses of radiation-resistant extremophiles (e.g. micro-organisms with the ability to survive in extreme environmental conditions) in biotechnology and the therapeutic industry. The major challenges of therapeutic development using extremophiles are discussed in [START_REF] Singh | Extremophiles: radiation resistance microbial reserves and therapeutic implications[END_REF].

Several in vitro and in silico works studied the causes of the high resistance of IRRB to ionizing radiation to determine peculiar features in their genomes and improve the treatment of radioactive wastes [START_REF] Needleman | A general method applicable to the search for similarities in the amino acid sequence of two proteins[END_REF]. However, limited computational works are provided for the prediction of bacterial IRR [START_REF] Sghaier | Basal DNA repair machinery is subject to positive selection in ionizing-radiation-resistant bacteria[END_REF] [START_REF] Makarova | Deinococcus geothermalis: the pool of extreme radiation resistance genes shrinks[END_REF]. In this work, we present some works that study the causes of the high resistance of IRRB to ionizing radiation. Then we focus on machine learning approaches that use protein sequences of bacteria to predict whether a bacterium belongs to IRRB or IRSB. These approaches formulate the problem of predicting bacterial IRR as an MIL problem where bacteria represent bags and repair proteins of each bacterium represent instances. MIL methods are a variation of machine learning methods that can be used to solve problems in which the labels are assigned to bags, i.e., a set of instances, rather than individual instances.

The remainder of this chapter is organized as follows. In Section 2, we present some computational works that aim to analyze IRRB in order to find out the causes of their resistance to ionizing radiation. In Section 3, we provide a formalization of the problem of MIL and explain how it could be used to solve the IRR prediction problem. Then we present some existing in silico approaches for IRR prediction in bacteria. Section 4 provides a brief comparison of the presented approaches. Concluding points make the body of Section 5.

Computational Works for Analyzing IRRB

Several in vitro and in silico works are proposed in order to study the causes of the high resistance of IRRB to ionizing radiation. In fact, determining the characteristics of IRRB could help to predict if a bacterium belongs to IRRB or IRSB. In this chapter, we present some of these works and show the pipeline of existent bioinformatics programs and the statistical methods they use.

In [START_REF] Sghaier | Basal DNA repair machinery is subject to positive selection in ionizing-radiation-resistant bacteria[END_REF], the authors analyze four known genome sequences of IRRB in order to find out the role of positive Darwinian selection in the evolution of IRR and the tolerance of desiccation. The used pipeline contains three steps:

Step 1. Finding orthologous relationships using MultiParanoid [START_REF] Alexeyenko | Automatic clustering of orthologs and inparalogs shared by multiple proteomes[END_REF].

Step 2. Aligning the sequences for each ortholog set using CLUSTAL W [START_REF] Thompson | CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice[END_REF].

Step 3. Testing for positive selection using the DnaSP program [START_REF] Librado | DnaSP v5: a software for comprehensive analysis of DNA polymorphism data[END_REF] that requires an aligned set of orthologous sequences. This work concludes that all basal DNA repair genes in IRRB are subject to positive selection unlike many of their orthologs in IRSB.

In [START_REF] Banerjee | Genomic and proteomic signatures of radiation and thermophilic adaptation in the Deinococcus-Thermus genomes[END_REF], the authors make a comparative analysis of codon and amino acid usage patterns. The study uses 19 genomes of the phylum Deinococcus-Thermus and follows a six-step pipeline.

Step 1. The authors make correspondence analysis on relative synonymous codon usage and amino acid usage using the program CodonW [START_REF] Peden | CodonW software[END_REF]. Then they use SPSS software [START_REF][END_REF] to make correlation and variance analysis.

Step 2. In order to find out the variation in amino acid usage between radiationsensitive and radiation-resistant genome of the studied bacteria, the STATIS-TICA software [START_REF]Statistica 6 software[END_REF] is used and a cluster analysis on amino acid usage is performed.

Step 3. To find out a cluster of orthologous proteins, the authors use the CMG-Biotools workbench [START_REF] Vesth | CMG-biotools, a free workbench for basic comparative microbial genomics[END_REF] and a BLAST matrix [START_REF] Altschul | Basic local alignment search tool[END_REF].

Step 4. Synonymous and non-synonymous substitution patterns in previously selected orthologous proteins are then estimated. The PAML software [START_REF] Yang | PAML 4: phylogenetic analysis by maximum likelihood[END_REF] is used in this step.

Step 5. Several indices are calculated in order to find out the factors influencing codon and amino acid usage including aromaticity, average hydrophobicity, isoelectric point and instability index.

Step 6. Finally, a COG [START_REF] Tatusov | The COG database: new developments in phylogenetic classification of proteins from complete genomes[END_REF] functional classification is performed in order to compare the proteins. The IMG/M system [START_REF] Markowitz | IMG/M: the integrated metagenome data management and comparative analysis system[END_REF] is used in this step as a support for comparative analysis of metagenomes.

This study reports significant differences in synonymous codon usage bias and amino acid usage patterns between the radiation-sensitive and radiationresistant genomes of the studied dataset.

In a recent work [START_REF] Shuryak | Quantitative modeling of microbial population responses to chronic irradiation combined with other stressors[END_REF], the authors identify general patterns of microbial responses to multiple stressors in radioactive environments. They analyze three datasets including a set of bacteria isolated from soil contaminated by nuclear waste at the Hanford site (USA) [START_REF] Fredrickson | Geomicrobiology of high-level nuclear wastecontaminated vadose sediments at the Hanford Site, Washington State[END_REF]. The other two datasets are out of the scope of this chapter since they concern fungi and yeasts. In order to develop a filter procedure for identifying important predictor variables, machine learning and information theoretic approaches are used. The pipeline contains three main steps.

Step 1. The authors start by testing the hypothesis which supposes that the collected contaminated soil samples are statistically dependent (samples separated by 1 meter of soil depth would contain the same bacterial taxa than samples separated by 10 meters). To do so, they use Mantel tests [START_REF] Mantel | The detection of disease clustering and a generalized regression approach[END_REF] for spatial autocorrelation using the ade4 R package [START_REF] Dray | The ade4 package: implementing the duality diagram for ecologists[END_REF].

Step 2. In order to find out the variables which are the least important for describing the data, authors use two machine learning prediction methods: random forests [START_REF] Breiman | Random forests[END_REF] and random generalized linear modeling [START_REF] Song | Random generalized linear model: a highly accurate and interpretable ensemble predictor[END_REF]. The variables that are identified as unimportant by both machine learning methods are most likely to be noise variables and are not used in the rest of the study.

Step 3. All variables are ranked in order of importance and filtered based on information theoretic approaches [START_REF] Burnham | Model selection and multimodel inference: a practical information-theoretic approach[END_REF] [START_REF] Burnham | AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons[END_REF]. A new model is created using the retained variables.

Multiple Instance Learning Approaches for Bacterial IRR Prediction

As far as we know, only three in silico approaches were proposed in order to predict the bacterial IRR based on a set of protein sequences. These approaches, named ABClass, ABSim and MIL naive approach [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF], are three machine learning algorithms that require as input a set of proteins sequences of each bacterium and provide as output a label response: IRRB if the query bacterium is radioresistant and IRSB if not. Since these approaches are based on a MIL formalisation, we present in this section the MIL problem formulation and we highlight some well known MIL algorithms. Then, we provide a description of the above cited approaches.

Problem Formulation

We denote Σ an alphabet defined as a finite set of characters or symbols. A symbolic sequence is defined as an ordered list of symbols [START_REF] Xing | A brief survey on sequence classification[END_REF]. The primary structure of a protein is a symbolic sequence since it is described using symbols (amino acids). Let DB be a learning database that contains a set of n labeled bags

DB = {(B i , Y i ), i = 1, 2 . . . , n} where Y i = {-1, 1}
is the label of the bag B i . Instances in B i are sequences and are denoted by B ij . Formally

B i = {B ij , j = 1, 2 . . . , m}
, where m is the total number of instances in this bag. We note that according to the problem investigated in this chapter, there is a relationship between instances of different bags since there are orthologous proteins in the different bags. This relation is denoted the across bag sequences relation in [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF]. The goal is to learn a multiple instance classifier from DB. Given a query bag Q = {Q k , k = 1, 2 . . . , q}, where q is the total number of instances in Q, the classifier should use sequential data in this bag and in each bag of DB in order to predict the label of Q.

Multiple Instance Learning: An Overview

In a traditional setting of supervised learning task, the training set is composed of feature vectors (instances), where each feature vector has a label. In MIL task, we learn a classifier based on a training set of bags, where each bag contains multiple feature vectors and it is the bag that carries a label [START_REF] Amores | Multiple instance classification: Review, taxonomy and comparative study[END_REF]. We do not know the labels of the instances inside the bags. The task of MIL investigated in this chapter is to learn a classifier from the training set that correctly predicts unseen bags. Several MIL algorithms have been proposed. A review of MIL approaches with a comparative study could be found in [START_REF] Amores | Multiple instance classification: Review, taxonomy and comparative study[END_REF] and [START_REF] Alpaydın | Single-vs. multiple-instance classification[END_REF]. A common assumption in MIL field is that a positive bag contains at least one positive instance, while in a negative bag all of the instances are negative. This assumption is called the standard multiple instance assumption. Several MIL algorithms adopt this asymmetrical assumption including MI-SVM [START_REF] Andrews | Support Vector Machines for Multiple-Instance Learning[END_REF] and Diverse Density [START_REF] Maron | A Framework for Multiple-Instance Learning[END_REF]. MI-SVM is an adaptation of support vector machines (SVM) to the MIL problem. The key point of Diverse Density algorithm is to find a concept point in the feature space that is close to at least one instance from every positive bag and meanwhile far away from instances in negative bags. Other methods adopt the so called collective assumption which states that all instances in a bag contribute to define its label. This assumption could be suitable to the problem investigated in this chapter since we do not know which set of proteins helps us to classify a bacterium as IRRB. Some algorithms make a positive instance selection. In a recent work [START_REF] Faria | MILKDE: A new approach for multiple instance learning based on positive instance selection and kernel density estimation[END_REF], the authors present the MILKDE algorithm which identifies the most representative instances in each positive bag based on a likelihood computation.

According to [START_REF] Amores | Multiple instance classification: Review, taxonomy and comparative study[END_REF], the MIL methods could be categorized according to how the information existent in the MI data is exploited. Three categories could be defined depending on the adopted paradigm:

• Methods following the instance-space paradigm assume that the discriminative information is present at the instance-level. We consider the characteristics of individual instances in the learning process without looking at more global characteristics of the whole bag. The simplest algorithm in this category is the SIL algorithm [START_REF] Bunescu | Multiple instance learning for sparse positive bags[END_REF] which trains a standard supervised classifier then simply uses the sum as aggregation rule to obtain the bag-level classifier.

• Methods following the bag-space paradigm treat each bag as a whole entity. A global bag-level information is used to make the discriminative decision instead of aggregating instance-level decisions. A commonly used approach is to define a distance function in order to compare bags.

In [START_REF] Wang | Solving the multiple-instance problem: A lazy learning approach[END_REF], the authors present an extension of the classical KNN algorithm [START_REF] Shakhnarovich | Nearest-neighbor methods in learning and vision[END_REF] called the Citation-kNN algorithm. It classifies a bag based on the labels of its neighbors (references and citers).

• Methods following the embedded-space paradigm map each bag to a feature vector which summarizes the relevant information about the whole bag. The bag-level information is extracted explicitly through the definition of a mapping function, while it is done implicitly in the bag-space paradigm. In [START_REF] Cheplygina | Multiple instance learning with bag dissimilarities[END_REF], the authors propose an MIL algorithm that computes the dissimilarities of a bag to other bags in the training set and uses these dissimilarities as a feature representation.

A Naive MIL Approach for IRR Prediction

In [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF], the authors present a naive MIL approach for sequence data with across bag relationships. Since the bacterial IRR prediction problem could be formal-ized as an MIL problem and there is a relationship between protein sequences across bags (orthologous proteins), then we can apply the naive approach in our case. This approach contains two steps: a preprocessing step and a learning step.

Step 1. The preprocessing step transforms the set of sequences into an attributevalue matrix where each row corresponds to a sequence and each column corresponds to an attribute. When we deal with sequence data, the most used technique to transform data into an attribute-value format is to extract motifs that serve as attributes. We note that finding a uniform description of all instances using a set of motifs is not always an easy task. Since the naive approach takes into account the across bag relationships between instances, the preprocessing step extracts motifs from each set of related instances. The union of these extracted motifs is then used as an attribute set to construct the descriptive matrix.

The presence or the absence of a motif in a sequence is respectively denoted by 1 or 0. It is worthwhile to mention that only a subset of the used attributes is representative for each processed sequence. Therefore, we may have a big sparse matrix when trying to present the whole sequence data using an attribute value format.

Step 2. The second step consists in applying an existing MIL classifier.

ABClass: Across Bag Sequences Classification Approach

In order to avoid the use of one large vector of features to describe sequence data, the ABClass approach [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF] that takes into account the across bag relationships between instances is proposed. It contains the following steps.

Step 1. A preprocessing step identifies orthologous protein sequences. Ideally, each protein has an orthologous sequence in each bag. This is defined as an across bag dependency. This relationship between sequences of different bags will be used in the learning step. The learning dataset is divided into sets of orthologous sequences. We note that a protein may not have any ortholog in a bag.

Step 2. A set of motifs is extracted from each set of orthologous sequences. In the experimental tests, DMS [START_REF] Maddouri | Encoding of Primary Structures of Biological Macromolecules Within a Data Mining Perspective[END_REF] is used as a motif extraction method. DMS allows building motifs that can discriminate a family of sequences from other ones. It first identifies motifs in the protein sequences. Then it filters them in order to keep only the discriminative and minimal ones.

Step 3. Extracted motifs are used to encode instances in order to create a dis-criminative model. Each set of related instances (i.e. orthologous proteins) is represented by its own motifs vector. This reduces the number of attributes that are not representative for the processed protein sequence. The WEKA [START_REF] Hall | The WEKA data mining software: an update[END_REF] data mining tool is used in order to apply existing well known classifiers to generate models. The following three classifiers have been used: SMO [START_REF] Platt | Fast training of support vector machines using sequential minimal optimization[END_REF] [42], J48 [START_REF] Quinlan | C4. 5: programs for machine learning[END_REF] and Naive Bayes [START_REF] John | Estimating continuous distributions in Bayesian classifiers[END_REF].

Step 4. To predict the IRR of an unlabeled bacterium, the extracted motifs are used to represent its instances. Each protein sequence is represented using a vector. Then it is compared with the corresponding model (already generated from its orthologous proteins) to provide a partial prediction result.

Step 5. Finally, an aggregation step is applied on the partial results in order to compute the final prediction result.

ABSim: Across Bag Sequences Similarity Approach

In [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF], the authors present ABSim, an algorithm that discriminates bags by measuring the similarity between each instance sequence in the query bag and corresponding related sequences in the different bags of the learning database.

ABSim is an extension of a previously proposed algorithm named MIL-Align [START_REF] Aridhi | Prediction of Ionizing Radiation Resistance in Bacteria Using a Multiple Instance Learning Model[END_REF]. The difference between these two algorithms is that ABSim is more general since MIL-Align was originally proposed to deal with biological data while ABSim aims to deal with MIL in sequence data in general e.g. textual data. When applied to the problem of bacterial IRR prediction, ABSim uses the local alignment score as similarity measure to compare protein sequences. The algorithm works as follows:

Step 1. For each protein sequence in the query bag, the algorithm computes the corresponding alignment scores between this protein and its orthologs in other bags.

Step 2. Alignment scores are grouped into a matrix. Each line corresponds to a score vector of a protein against all its orthologs in other bacteria.

Step 3. An aggregation method is applied to the matrix in order to compute the final prediction result. Two aggregation methods named SMS and WAMS are proposed by the authors.

Experimental Results of MIL Approaches

The MIL naive approach, ABClass and ABSim are used in [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF] in order to resolve the problem of phenotype prediction of bacterial IRR. Bacteria rep-resent the bags and primary structure of basal DNA repair proteins represent the sequences. An unknown bacterium is affiliated to either IRRB or IRSB. The used dataset is described in [START_REF] Aridhi | Prediction of Ionizing Radiation Resistance in Bacteria Using a Multiple Instance Learning Model[END_REF]. It consists of 28 bacteria (14 IRRB and 14 IRSB). Each bacterium/bag contains 25 to 31 instances that correspond to proteins implicated in basal DNA repair in IRRB. Proteins of the bacterium Deinococcus radiodurans were downloaded from the UniProt website. Proteomes of other bacteria were downloaded from the NCBI FTP website. ABSim and ABClass tools can be downloaded at the following link: http://homepages.loria.fr/SAridhi/software/MIL/.

It is worthwhile to mention that ABClass is tested under several different settings (classifiers and motif extraction settings) and that the obtained accuracy results depend on the used settings. The over all accuracy results reported in [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF] are very close but a slightly better accuracy rates are provided either by ABClass or by ABSim according to the used settings. Using both approaches, two bacteria (M. radiotolerans and B. abortus) generate the lowest rates of successful prediction compared to the rate of the other bacteria. These results may help to understand some characteristics of the studied data. A probable biological explanation is provided in [START_REF] Aridhi | Prediction of Ionizing Radiation Resistance in Bacteria Using a Multiple Instance Learning Model[END_REF] and notes that this could be explained by the increased rate of sequence evolution in endosymbiotic bacteria [START_REF] Woolfit | Increased rates of sequence evolution in endosymbiotic bacteria and fungi with small effective population sizes[END_REF].

Comparison

Table 4.1 provides a short comparison of the previously presented approaches. The three works [START_REF] Sghaier | Basal DNA repair machinery is subject to positive selection in ionizing-radiation-resistant bacteria[END_REF] [20] and [START_REF] Banerjee | Genomic and proteomic signatures of radiation and thermophilic adaptation in the Deinococcus-Thermus genomes[END_REF] are interested in analyzing different characteristics of IRRB. The works in [START_REF] Sghaier | Basal DNA repair machinery is subject to positive selection in ionizing-radiation-resistant bacteria[END_REF] and [START_REF] Banerjee | Genomic and proteomic signatures of radiation and thermophilic adaptation in the Deinococcus-Thermus genomes[END_REF] are based on a pipeline that uses existent bioinformatics programs in order to perform their studies. The study in [START_REF] Makarova | Deinococcus geothermalis: the pool of extreme radiation resistance genes shrinks[END_REF] is based on a filter of machine learning and information theoretic approaches. Although these works are important to understand the causes of the high resistance of IRRB to ionizing radiation, they do not provide a tool to predict if an unknown bacterium belongs to IRRB or IRSB.

The naive MIL approach, ABClass and ABSim provide as output a prediction label for an unknown bacterium (IRRB or IRSB). The naive MIL approach uses standard MIL classifiers after making a preprocessing step which extracted motifs and adapt the data to the required format. This preprocessing step is time consuming and could lead to a huge matrix. ABCLass takes advantage of the across bag relationships between sequences in order to reduce the number of attributes that are not representative for each sequence during the encoding [START_REF] Sghaier | Basal DNA repair machinery is subject to positive selection in ionizing-radiation-resistant bacteria[END_REF] Analysis of IRRB Pipeline Banerjee et al., 2014 [START_REF] Banerjee | Genomic and proteomic signatures of radiation and thermophilic adaptation in the Deinococcus-Thermus genomes[END_REF] Analysis of IRRB Pipeline Shuryak and Dadachova, 2016 [START_REF] Shuryak | Quantitative modeling of microbial population responses to chronic irradiation combined with other stressors[END_REF] Analysis of IRRB Information theory and machine learning MIL Naive Approach [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF] IRR Prediction MIL classifiers and motif extraction ABClass [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF] IRR Prediction MIL model and optimized use of motifs ABSim [START_REF] Zoghlami | A multiple instance learning approach for sequence data with across bag dependencies[END_REF] IRR Prediction MIL model and alignment score step. This relationship is also used during the learning step when generating partial models for each set of related sequences. ABSim does not use motifs to represent data since no encoding step is needed. The local alignment score is used to perform the prediction. This makes ABSim faster and easier to use than ABClass unless we already have the representative motifs for each set of orthologous proteins or if we think that the extraction of motifs will not be an expensive task (according to the data size, the used motifs extractor and the extraction settings e.g. required motifs length). As mentioned in the previous section, a slightly better accuracy result could be provided either by ABClass or by ABSim according to the used settings.

Conclusion

Prediction of IRR in bacteria is a challenging task. Several works were interested in finding out the causes of the resistance of some bacteria to IRR. These works generally use a pipeline of existing bioinformatics programs. Other works provide machine learning algorithms in order to predict the bacterial IRR. They are based on an MIL formalization. In this chapter, we studied existing works on prediction of IRR in bacteria and we presented a comparison of the studied approaches. Based on our study, we mention that the used settings in the preprocessing step and the learning step influence the choice of the approach to use.

Table 4 .

 4 1. Comparison of the presented approaches on IRR analyses\prediction in bacteria.

	Approach	Task	Method
	Sghaier et al., 2008


Mohamed Khemakhem

Laurent Romary

Simon Gabay

Hervé Bohbot

Francesca Frontini

Giancarlo Luxardo

Au

Automatically Encoding Encyclopedic-like Resources in TEI

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

Automatically Encoding Encyclopedic-like Resources in TEI

Mohamed Khemakhem1,2,3 , Laurent Romary [START_REF] Khemakhem | Automatic Extraction of TEI Structures in Digitized Lexical Resources using Conditional Random Fields[END_REF][START_REF] Khemakhem | Enhancing Usability for Automatically Structuring Digitised Dictionaries[END_REF]4 {name.surname@inria.fr} 1 Inria ALMAnaCH, Paris [START_REF] Khemakhem | Enhancing Usability for Automatically Structuring Digitised Dictionaries[END_REF] Centre Marc Bloch, Berlin 3 Paris Diderot University, Paris 4 BBAW -Berlin-Brandenburgische Akademie der Wissenschaften, Berlin Simon Gabay {surname.name@unine.ch} Université de Neuchâtel -Institut de littérature française Hervé Bohbot, Francesca Frontini, Giancarlo Luxardo {name.surname@univ-montp3.fr} Univ Paul Valéry Montpellier 3, CNRS, PRAXILING UMR 5267 Encyclopedic content exists in different forms of paper-based resources and remains to a very large extent not exploited given the limited alternatives to extract information from the corresponding digitized material. Where TEI has provided mechanisms for encoding such a content, recent works have yielded advanced techniques to apply these mechanisms automatically on raw resources, however clear recommendations for the encoding of such content is still lacking.

As current digitization projects concern encyclopedias, other projects are undertaken to digitize textual resources with heritage significance and with similar features in terms of layout and indexed access. In this paper we introduce new lexicographic models, customizing the TEI schema, we extend existing ones and we present their application on two categories of resources, currently under development to be made available for public use:

• Encyclopedic sections of early, out of copyright, versions of a reference French Dictionary (Petit Larousse Illustré), • Manuscripts auction catalogues, which are old resources for referencing and semantically describing manuscripts for sale.

The definition of these models is based on the significant similarities noticed at different levels of the described information in such entry-based resources. We have employed elements from the TEI dictionaries module to enable the segmentation of morphological and semantic information encompassed by respectively <form> and <sense> elements, already extracted by dedicated existing models in GROBID-Dictionaries 1 's architecture. In fact, each entry in both types of resources carries two main encyclopedic information. First, the name or the label of a concept, coupled with one or more of its extended form and coming sometimes with a brief description. Then, a second block comes to establish an exhaustive description of the concept and to present related information such as bibliography or pricing. In addition, we have used a customized version of the <entry> element to allow the generic encoding of entry numbering (see second excerpt in the table below).

TEI encoding

  Ch.-L. de)</addName>, <desc>le plus brillant général de cavalerie des guerres de la République et de l'EmpIre, né à Metz, tué à la bataille de Wagram</desc> </form> <sense> .-<def> <bibl>L. a. s. au général Dugua; 1 p. inf.</bibl> <num type="price">10 »</num> </def> <note>Superbe lettre sur la campagne d'Egypte. Il profite du départ du général Desaix pour lui donner des nouvelles. Desaix lui laisse le commandement de la colonne qui doit poursuivre Mourad-Bey, et qui se compose de 400 hommes de cavalerie, 4 pièces de canon et 160 dromadaires. Le général Boyer a, dans une petite affaire, tué 10 mameloucks et 40 arabes, etc.</note> </sense> </entry>

Excerpt from Dictionary Encyclopedic Section in Petit Larousse Illustré (1948)

	<entry>
	<form type="lemma">
	<persName>ABERDEEN</persName>
	<addName>(G. H. Gordon, comte
	d')</addName><pc>,</pc>
	<desc>homme d'Etat anglais, né à
	Edimbourg</desc>
	</form>
	<pc>.</pc>
	<sense>
	<def>Premier ministre en

1852, il conclut avec la France une alliance contre la Russie (1784- 1860)</def> </sense> <pc>.</pc> </entry> ِ ◌Excerpt from a Manuscripts Auction Catalogue (1889)

	<entry>
	<num>49</num>
	<form type="lemma">
	<surName>Kourakin</surName>
	<addName>(le prince Alexis
	B.),</addName>
	<desc> frère du précédent, homme d'Etat
	russe.</desc>
	</form>
	<sense>
	<pc>-</pc>
	<def>
	<bibl>Billet auto sig., en francais, à M.
	Monférand, 1 p, in-8.</bibl> <num type="price">2
	»</num>
	</def>
	</sense>
	</entry>

https://github.com/MedKhem/grobid-dictionaries/

We employed the adapted and newly defined models to automatically process and label the encyclopedic information in a cascading fashion, as introduced in Khemakhem et al. 2017 and Khemakhem et al. 2018, by relying on the same sequence labeling machine learning technique.

We will present in-depth our progress in implementing morphological and semantic models and show through the results at each structuring level how such information could be uniformly encoded and automatically extracted from these resources.


R Cox

M J Wenzel

F Josse

S M Heinrich

I Dufour

Generalized Characteristics of Resonant Polymer-Coated Microcantilevers in Viscous Liquid Media

Expressions describing the resonant frequency and quality factor of a dynamically-driven, polymer-coated microcantilever in a viscous liquid medium have been obtained. These generalized formulas are used to describe the effects the operational medium and the coating has on the device sensitivity when used in liquid-phase chemical sensing applications. The derived expressions are shown to reduce to well-known formulas for the case of an uncoated cantilever in an invisicid medium and the case of a coated cantilever in air. The theoretical results are compared to existing chemical sensor data in aqueous and viscous solutions.

I. INTRODUCTION

Polymer-coated microcantilevers have been extensively investigated for use as chemical sensor platforms [START_REF] Sampath | Analytical Modeling of Microcantilever-Based Dynamic Microsensors[END_REF][START_REF] Sampath | Study of Viscoelastic Effect on the Frequency Shift of Microcantilever Chemical Sensors[END_REF][START_REF] Vancura | Liquid-Phase Chemical and Biochemical Detection Using Fully Integrated Magnetically Actuated Complementary Metal Oxide Semiconductor Resonant Cantilever Sensor Systems[END_REF][START_REF] Lochon | Silicon made resonant microcantilever: Dependence of the chemical sensing performances on the sensitive coating thickness[END_REF]. Microcantilevers have shown high sensitivities in chemical vapor detection due to their high surface area to mass ratio. Application of microcantilevers to liquid-phase detection has mostly focused on static mode detection because dynamicallydriven microcantilevers suffer from low frequency stability in viscous media [START_REF] Pinnaduwage | Moore's Law in Homeland Defense: An Integrated Sensor Platform Based on Silicon Microcantilevers[END_REF].

The characteristics of uncoated dynamically-driven microcantilevers have been previously investigated in viscous media [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF]. Recently, work has been done on characterizing the behavior of polymer-coated microcantilevers in a vacuum, which indicated significant chemically induced coating plasticization effects [START_REF] Sampath | Analytical Modeling of Microcantilever-Based Dynamic Microsensors[END_REF]. However, the effects of the polymer coating in a viscous liquid environment have not been studied. The present derivation extends previous work on uncoated and coated microcantilevers to obtain generalized formulas for the characteristics of a polymer-coated microcantilever operating in a viscous liquid medium.

II. THEORY

A. Generalized Equation of Motion

Figure 1 shows the length, L, width, b, and thickness, h 1 , of the microcantilever as well as the polymer layer's thickness, h 2 .

The deflection function, w(x,t), which represents the vertical displacement along the length of the beam as a function of time is also indicated.

Assuming that the microcantilever is a rectangular beam with L>>b, b>h 1 and b>h 2 , undergoing small lateral deformations, the well-known equation of motion for an uncoated microcantilever operating in a vacuum is given by

t j B e x F t t x w m x t x w EI ω ) ( ) , ( ) , ( 2 2 4 4 = ∂ ∂ + ∂ ∂ , (1)
where EI and m B are the beam's flexural rigidity and mass per unit length, respectively, and F(x) is the position dependent forcing function per unit length operating at a angular frequency of ω [START_REF] Sampath | Analytical Modeling of Microcantilever-Based Dynamic Microsensors[END_REF]. Using the modifications to the equation of motion found in [START_REF] Sampath | Analytical Modeling of Microcantilever-Based Dynamic Microsensors[END_REF] and [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF], a generalized equation of motion for a polymer-coated microcantilever in an unbounded, viscous liquid medium is given by

t j B e x F t t x w m x t x w EI ω ) ( ) , ( * ) , ( * ) ( 2 2 4 4 = ∂ ∂ + ∂ ∂ , (2)
where m B * is the effective mass per unit length and the flexural rigidity of the polymer-coated microcantilever is [START_REF] Sampath | Analytical Modeling of Microcantilever-Based Dynamic Microsensors[END_REF] Figure 1: A rectangular microcantilever shown with a polymer layer

θ j e EI EI EI         + = 2 2 ' ' ) ( ' ) ( * ) ( (3)
with ( )

      ′ + = 2 2 1 1 ' I E I E EI , (4) and ( )
      ″ = 2 2 ' ' I E EI . ( 5
)
E 1 is the Young's modulus of the base layer, E ′ 2 and E ″ 2 are the storage modulus and loss modulus of the polymer layer, respectively, and I 1 and I 2 are the moment of inertia of the base and polymer layer, respectively. For a system with a polymer layer, the moment of inertia can be calculated using a time-invariant neutral axis approximation [START_REF] Sampath | Analytical Modeling of Microcantilever-Based Dynamic Microsensors[END_REF]. For composite base-layer microcantilevers, such as a CMOS based cantilever, the flexural rigidity can be found by replacing E 1 I 1 in eq. ( 4) with the sum of each layer's flexural rigidity [START_REF] Lange | Complementary Metal Oxide Semiconductor Cantilever Arrays on a Single Chip: Mass-Sensitive Detection of Volatile Organic Compounds[END_REF]. θ in eq. ( 3) is the composite loss angle of the beam, and is defined as

( ) ( )         ′ + ″ = - ω ω θ 2 2 1 1 2 2 1 tan E h E h E h . (6)
Here, the dependence of E ′ 2 and E ″ 2 on the operating frequency has been explicitly stated.

The effective mass per unit length, m B * , accounts for both the mass of the coated-cantilever and the displaced mass of the fluid, as well as the viscous damping caused by fluid shear near the edges of the microcantilever [START_REF] Basak | Hydrodynamic loading of microcantilevers vibrating in viscous fluids[END_REF]. The viscous damping is represented by g 1 , given by ω ρ π

) ( 4 2 1 Re b g i L Γ = , (7)
and the mass of the displaced fluid is represented by g 2 , given by [START_REF] Dufour | Theoretical analysis of strongaxis bending mode vibrations for resonant microcantilever (bio)chemical sensors in gas or liquid phase[END_REF] ) ( 4

2 2 Re b g r L Γ = ρ π . ( 8
)
Here, ρ L is the density of the medium and Γ r (Re) and Γ i (Re) are the real and imaginary components of the hydrodynamic function, Γ(Re), of the microcantilever, given by

        - - + Ω = Γ ) ( ) ( 4 1 ) ( ) ( 0 1 jRe j K jRe jRe j jK Re Re . (9)
In eq. ( 9), Ω(Re) is the function used to correct the hydrodynamic function of a beam of circular cross section, Γ circ (Re), to that of a rectangular beam [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF]. K 0 and K 1 are modified Bessel functions. The hydrodynamic function is dependent on the Reynolds number [START_REF] Basak | Hydrodynamic loading of microcantilevers vibrating in viscous fluids[END_REF], which is a measure of the ratio of inertial forces to the viscous forces acting on the beam, and is defined as

L L b Re η ω ρ 4 2 = , (10)
where η L is the viscosity of the fluid. The force exerted by the fluid is a sum of the viscous force and the inertial forces,

∂ ∂ - ∂ ∂ - = . ( 11
)
Assuming a sinusoidal deflection function, eq. ( 11) can be converted to fit the form of eq. ( 2), resulting in the effective mass per unit length given by

( ) φ ω j B e g g L m m 2 1 2 2 *       + + = , (12)
where ( )

        + - = - 2 1 1 / tan Lg m g L ω φ . ( 13
)
and m is the mass of the microcantilever with the coating.

B. Generalized Resonant Frequency

The resonant frequency of a coated-microcantilever in a viscous medium can be found using the generalized equation of motion, eq. ( 2). It is commonly assumed that the Young's modulus of the base layer is frequency-independent. For the polymer layer, the Young's modulus depends on the frequency. However, a first approximation can be taken equal to its value taken at the operating resonant frequency. The Reynolds number of the system is linearly proportional to the resonant frequency. This dependence must be considered whenever the viscous forces are significant (i.e., relatively small Reynolds numbers). Assuming a frequencydependent hydrodynamic function, the resonant frequency obtained by solving eq. ( 2) is given by

M K L f i i res 2 2 , 2π α = ( 14
)
where i α is the ith root of 0 1 ) cosh( ) cos( = - i i α α , ( 15
) ( ) ′′                     +       - ′               + + = ) ( 2 ) ( 2 1 1 2 2 EI g d d g EI g d d g L m K ω ω ω ω ω ω , (16)
( ) ( )

2 2 2 1 1 1 2 2 g L m g d d g L m g g d d g M +               + + +                           +       = ω ω ω ω ω ω ω , ( 17
) ) ( 4 2 1 Re b g d d i L Λ =       ρ π ω ω , (18)
( )

) ( 4 2 2 Re b g d d r L Λ = ρ π ω , (19)
and Λ r (Re) and Λ i (Re) are the real and imaginary components of Λ(Re), which is the defined as the derivative of the hydrodynamic function. This function can be obtained as

( ) ( ) ( ) ( ) ) 20 ( . ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 ) ( 2 0 0 2 2 1 Re d d Re jRe j K jRe j K jRe j K jRe j K Re Re circ Ω Γ +           - - - - - Ω = Λ ω ω Λ(Re)
is only dependent on the Reynolds number since Ω(Re) also has a derivative inversely proportional to ω .

Through the use of an iterative process, eq. ( 14) can be solved. Iterative correction uses an initial guess for ω (for example, the resonant frequency in a vacuum). A value for the Reynolds number can then be calculated, which in turn can be used to update the value of the ω.

If both the Young's modulus of the polymer layer and the Reynolds number are assumed frequency-independent near resonance, the resonant frequency can be simplified to

( )( ) ( ) ( ) 2 1 2 2 1 2 2 2 , ' ' ' 2       + +       - + = ω ω π α g g L m EI g EI g L m L f i i res . ( 21
)
It can be shown that both eq. ( 14) and eq. ( 21) reduce to the well-known expression for the resonant frequency of a coated-microcantilever in a vacuum (g 1 =g 2 =0) [START_REF] Sampath | Study of Viscoelastic Effect on the Frequency Shift of Microcantilever Chemical Sensors[END_REF], given by

m I E I E L f 2 2 1 1 2 / 3 2 0 0 2 ′ + = π α . ( 22
)
with α 0 ≅ 1.875 corresponding to the fundamental flexural mode.

If there are only small dissipative effects from both the medium and the polymer in a viscous liquid medium, the resonant frequency simplifies to

m Lg f f res 2 0 1 1 + = . ( 23
)
This is equivalent to the resonant frequency obtained in [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF]. When the medium is assumed inviscid, eq. ( 23) can be further simplified to a form analogous to the one presented in [START_REF] Lindholm | Elastic vibration Characterisitcs of Cantilever Plates in Water[END_REF] as

( ) m b L f f L res 4 1 1 2 0 πρ + = .
(24)

C. Quality Factor

Operation in a viscous liquid medium drastically decreases the frequency stability of microcantilevers in an oscillator configuration. Equation ( 2) can be used to calculate the quality factor of the system. Because it is difficult to obtain an analytical expression for the quality factor, it is best solved numerically. This is done by calculating the upper and lower 3 dB frequencies through an iterative process.

If both the Young's modulus of the polymer layer and the Reynolds number are again considered constant in the range of operational frequencies, the quality factor can be obtained from eq. ( 2) as

( ) ( )( ) ( )( ) ( ) 1 1 2 2 1 ' ' ' ' ' ' 1 1 2 -                                   - + + +       - - = EI g EI g L m EI g L m EI g Q ω ω . ( 25
)
The above approximation is found to be in good agreement with the numerically derived generalized quality factor for Re>>1. Assuming operation in a vacuum, g 1 and g 2 are both zero and eq. ( 25) reduces to the one presented in [START_REF] Sampath | Analytical Modeling of Microcantilever-Based Dynamic Microsensors[END_REF],

( ) ( ) 1 0 '' 2 1 1 ' EI Q EI -         = --             . ( 26
)
In low loss systems, eq. ( 25) can further be approximated as

( )( ) ( ) ( ) ( )( ) ' ' ' ' ' ' 2 1 1 2 EI g L m EI g EI g EI g L m Q approx + +             - + = ω ω . ( 27
)
For an uncoated cantilever, eq. ( 27) reduces to the estimation of the quality factor in low loss from [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF]. Other losses can be added into the quality factor by the well-known equation for dealing with multiple loss systems, as

∑ = i i sum Q Q 1 1 . ( 28
)
Q i is the quality factor associated with a particular loss source.

In practical applications, the losses caused by the medium and the polymer coating are normally the dominant terms. Using eq. ( 28), taking only into account these losses, the quality factor can be approximated as 27) reduces to eq. (29).

( ) ( ) ( ) 1 2 1 ' ' ' -             + +       = EI EI g L m g Q sum ω (29) When ( ) ' ' 1 EI g       ω is negligible, eq. (
Under certain conditions, other losses, such as from the squeeze film effect or clamping, can significantly contribute to the decrease of the quality factor [START_REF] Basak | Hydrodynamic loading of microcantilevers vibrating in viscous fluids[END_REF].

D. Effects of Chemical Analyte Soption into the Coating

Introduction of a chemical analyte into the operational medium will not only change the medium's viscosity and density, but will also affect the characteristics of the coated microcantilever through chemical sorption into the polymer layer. For example, the density and thickness of the polymer layer will increase; the moment of inertia for both layers will change due to a shift in the neutral axis; and the complex Young's moduli of the polymer layer will change. While these effects on the resonant frequency, f res , are generally assumed negligible, they can be significant in the determination of ∆f res . This shift in the resonant frequency in turn can be used to determine the chemical concentration of the analyte in the medium.

The change in the viscosity and density of the solution can be accounted for by differential measurement using an uncoated reference cantilever of the same geometry; therefore, these effects will not be included in the discussion herein. Assuming only small variations in the system, the shift in the resonant frequency can be found as a function of the change in microcantilever mass, ∆m, changes in storage and loss modulus, ∆E ′ 2 and ∆E ″ 2 , and changes in the moments of inertia ∆I 1 and ∆I 2 as

2 1 2 2 2 1 2 2 I I E E m f I I E E m res ∆ + ∆ + ′′ ∆ + ′ ∆ + ∆ ≅ ∆ ′′ ′ λ λ λ λ λ . (30)
In eq. ( 30), the λ terms describe the sensitivities to various changes in the system, and are given as

( ) ( ) ( ) ( ) 1 1 1 1 1 2 2 2 2 2 2 2 2 2 m r e s d g g g EI d KLM d g g m g EI L d f KLM d m g g L d LM ω ω ω ω ω ω ω ω ω λ ω ω     ′         +                               ′′         + +                   = +           + +             -         (31a) ( ) 2 2 2 2 2 2 res E d m I g g f L d K ω ω λ ′     + +         = (31b) 2 1 1 2 2 2 res E d g g I f d K ω ω ω ω λ ′′         - +                 = (31c) ( ) 1 1 2 2 2 2 I res d m E g g f L d K ω ω λ     + +         = (31d) and ( ) 2 2 2 2 1 1 2 2 2 2 2 I res d m E g g L d K f d g g E d K ω ω λ ω ω ω ω       ′ + +               =       ′′       +                   -     . ( 31e
)
It is noted that the swelling induced change in the polymer thickness is included in the ∆I terms. All other terms (terms including ∆ products) have been assumed negligible for small frequency shifts. Also, eq. (31d) and eq. (31e) show that shifts in the moment of inertia can be disregarded. This is similar to what was shown in [START_REF] Sampath | Study of Viscoelastic Effect on the Frequency Shift of Microcantilever Chemical Sensors[END_REF]. Equations ( 30) and (31) can then be used to analyze the sensitivity response of coated microcantilever chemical sensors.

III. RESULTS

A. Simulations

Simulations are performed to illustrate the effects of coating and medium properties for various microcantilever geometries. The polymer layer used in these simulations is polyisobutylene (PIB). The Young's modulus for PIB has been previously characterized in [START_REF] Ferry | Viscoselastic Properties of Polymers[END_REF]. Figure 2 and3 shows the frequency response of a polymer-coated microcantilever to different aqueous mixtures of glycerol and ethanol, respectively.

For low Reynolds numbers, Re, i.e. high viscosity fluid and/or low density, the results indicate that the hydrodynamic function cannot be considered frequency-independent. Therefore, g 1 and g 2 must be considered frequency dependent in calculating the resonant frequency. Figure 3 indicates that the resonant frequency is not just dependent on the viscosity, but the overall Reynolds number. While ethanol has a higher viscosity compared to water, its higher fluid density leads to an overall higher Reynolds number and resonant frequency.

The calculated quality factor using the upper and lower 3 dB frequencies and eq. ( 25) shows a negligible difference in water and glycerol. Figures 4 and5 compare the calculated quality factor with that of low loss approximation using eq. ( 27). As expected, eq. ( 27) is shown to be inappropriate for high viscosity media. The difference between the approximation and the exact calculation is found to increase as the Reynolds number decreases. In the calculations, it is assumed that the Young's modulus of the coating does not change as a function of the operational medium. Chemical absorption into the polymer coating is then simulated assuming an increase of polymer mass by up to 5% (45.85 pg), a storage modulus decrease by up to 10% (-6.73 MPa), and a loss modulus increase by up to 100% (+102.48 MPa) (Figs. 6 and7). The mass absorption is found to cause up to a 42 Hz decrease in the resonant frequency in water, whereas the coating plasticization effects contribute up to an additional 9.9 Hz decrease in the resonant frequency. In 40% glycerol (~3.6 cP), the same mass loading causes up to a 23.9 Hz decrease in the resonant frequency, whereas the coating plasticization effects contribute an additional 11.7 Hz decrease in the resonant frequency. This indicates that the sensitivity to mass loading decreases in higher viscosities solutions, while the sensitivity to changes in the Young's modulus increases in higher viscosities.

B. Comparison to Experimental Data

Recently performed experiments have shown the feasibility of dynamically-driven CMOS multilayer microcantilever chemical sensors in liquid environments [START_REF] Vancura | Liquid-Phase Chemical and Biochemical Detection Using Fully Integrated Magnetically Actuated Complementary Metal Oxide Semiconductor Resonant Cantilever Sensor Systems[END_REF]. With a reference microcantilever to account for the effects of the medium, the response of a 150x140x8.2 µm CMOS-based microcantilever coated with 0.3 µm of PIB to 350 ppm ethylbenzene was found to result in a shift in the resonant frequency of about 85 Hz. However, the theoretical model used in [START_REF] Vancura | Liquid-Phase Chemical and Biochemical Detection Using Fully Integrated Magnetically Actuated Complementary Metal Oxide Semiconductor Resonant Cantilever Sensor Systems[END_REF] assuming only mass loading predicted a 63 Hz shift in the resonant frequency.

For this cantilever geometry since the condition L>>b is not satisfied, shearing effects can no longer be considered negligible. For the associated fluid properties, the Reynolds number is quite large, i.e. Re>>1. Using eq. ( 23), g 2 can be obtained as

L m f f g res         -         = 1 2 0 2 . ( 32
)
Using the measured resonant frequencies, f 0 and f res , in air and the liquid, respectively, g 2 , can be empirically extracted from eq. ( 32), and g 1 can be assumed zero.

Using eq. (30a) and the frequency shift from mass loading, the decrease in the resonant frequency due to mass absorption alone is 63 Hz at a concentration of 350 ppm. Assuming up to a -70% decrease in storage modulus and up to a 700% increase in loss modulus, an additional 7 Hz decrease in the resonant frequency can be accounted for by coating plasticization (Fig. 8). [START_REF] Vancura | Liquid-Phase Chemical and Biochemical Detection Using Fully Integrated Magnetically Actuated Complementary Metal Oxide Semiconductor Resonant Cantilever Sensor Systems[END_REF] for the resonant frequency shift of a 150x140x8.2µm microcantilever coated with 0.3 µm of PIB to the theoretically calculated frequency shift taking into account first mass absorption and then mass absorption and plasticization effects. Note that a reference cantilever is used in [START_REF] Vancura | Liquid-Phase Chemical and Biochemical Detection Using Fully Integrated Magnetically Actuated Complementary Metal Oxide Semiconductor Resonant Cantilever Sensor Systems[END_REF] to account for the effects of changes in the medium properties.

IV. CONCLUSIONS

Generalized equations for the resonant frequency and quality factor of a dynamically driven, polymer-coated microcantilever accounting for the effects of the medium and the polymer coating have been presented. It is found that the resonant frequency and quality factor can be significantly affected by non-mass loading effects. It is also found that the resonant frequency's sensitivity to mass loading and other system properties are dependent on the medium of operation. The generalized equations obtained in this work simplify to known special cases and can be used to estimate the contribution of non-mass absorption effects in the response of dynamically-driven microcantilever chemical sensors.

Figure 2 :Figure 3 :

 23 Figure 2: Calculated resonant frequency of a 100x20x2 µm microcantilever coated with 0.5 µm of PIB in varying mixtures of glycerol (up to 64%, or 18 cP)

Figure 4 :Figure 5 :

 45 Figure 4: Calculated quality factor of a 100x20x2 µm microcantilever with a 0.5 µm PIB coating in varying mixtures of glycerol (up to 64%) compared with the small loss approximation Qapprox

Figure 6 :Figure 7 :

 67 Figure 6: Shifts in the resonant frequency of a 100x20x2 µm microcantilever with a 0.5 µm PIB coating in water undergoing mass absorption of up to 45 pg with and without coating plasticization effects

Figure 8 :

 8 Figure 8: Comparison of experimentally measured values in[START_REF] Vancura | Liquid-Phase Chemical and Biochemical Detection Using Fully Integrated Magnetically Actuated Complementary Metal Oxide Semiconductor Resonant Cantilever Sensor Systems[END_REF] for the resonant frequency shift of a 150x140x8.2µm microcantilever coated with 0.3 µm of PIB to the theoretically calculated frequency shift taking into account first mass absorption and then mass absorption and plasticization effects. Note that a reference cantilever is used in[START_REF] Vancura | Liquid-Phase Chemical and Biochemical Detection Using Fully Integrated Magnetically Actuated Complementary Metal Oxide Semiconductor Resonant Cantilever Sensor Systems[END_REF] to account for the effects of changes in the medium properties.