Orves Honoré D'estienne D'

Alan Bâtiment

Turing

Mélina Gallopin

Gilles Celeux

Florence Jaffrézic

Andrea Rau

A model selection criterion for model-based clustering of annotated gene expression data

Keywords: Functional gene annotation, gene expression data, model-based clustering, model selection Annotations fonctionnelles des gènes, données d'expression géniques, classification par modèle de mélange, sélection de modèle

In co-expression analyses of gene expression data, it is often of interest to interpret clusters of co-expressed genes with respect to a set of external information, such as a potentially incomplete list of functional properties for which a subset of genes may be annotated. Based on the framework of finite mixture models, we propose a model selection criterion that takes into account such external gene annotations, providing an efficient tool for selecting a relevant number of clusters and clustering model. This criterion, called the Integrated Completed Annotated Likelihood (ICAL), is defined by adding an entropy term to a penalized likelihood to measure the concordance between a clustering partition and the external annotation information. The ICAL leads to the choice of a model that is more easily interpretable with respect to the known functional gene annotations. We illustrate the interest of this model selection criterion in conjunction with Gaussian mixture models on simulated gene expression data and on real RNA-seq data.

Introduction

Genome annotation broadly refers to the set of meta-data associated with the coding regions in the genome, typically including the identification of the location of each gene as well as a determination of the functions related to the gene product (e.g., protein or RNA). In particular, gene annotations correspond to known functions related to the gene product, including molecular functions, biological pathways, or the cellular location of the gene products. A variety of well-known unified databases have been constructed with known functional annotations collected from bibliographic sources across species, including the Gene Ontology (GO) [START_REF] Ashburner | Gene ontology: tool for the unification of biology. The Gene Ontology Consortium[END_REF], the Kyoto Encyclopedia of Genes and Genomes (KEGG) [START_REF] Kanehisa | KEGG: kyoto encyclopedia of genes and genomes[END_REF] or the MSigDB (Molecular Signatures) databases [START_REF] Liberzon | Molecular signatures database (MSigDB) 3.0[END_REF]. Although such databases contain a rich source of functional information about the genome in a large variety of species (e.g., Arabidopsis thaliana, human, rat, mouse, fly), our knowledge of functional annotations is often far from complete [START_REF] Tipney | An introduction to effective use of enrichment analysis software[END_REF].

In recent years, substantial improvements in high-throughput technologies, such as microarrays [START_REF] Schena | Quantitative monitoring of gene expression patterns with a complementary DNA microarray[END_REF] and more recently RNA sequencing (RNA-seq) [START_REF] Mortazavi | Mapping and quantifying mammalian transcriptomes by RNA-Seq[END_REF], have enabled the simultaneous measurement of the expression levels of tens of thousands of genes. A rich body of work is now available on the appropriate statistical analyses of such gene expression data, including the analysis of differential expression [START_REF] Smyth | Linear models and empirical Bayes methods for assessing differential expression in microarray experiments[END_REF][START_REF] Anders | Differential expression analysis for sequence count data[END_REF] and co-expression analyses to identify groups of genes with similar profiles across several experimental conditions or over the course of time [START_REF] Yeung | Model-based clustering and data transformations for gene expression data[END_REF][START_REF] Rau | Co-expression analysis of high-throughput transcriptome sequencing data with Poisson mixture models[END_REF]. The latter is of particular interest in this work, as identifying genes that share the same dynamic patterns of expression may help identify groups of genes that are involved in similar biological processes and generate hypotheses about the functional properties of poorly characterized genes [START_REF] Eisen | Cluster analysis and display of genome-wide expression patterns[END_REF][START_REF] Jiang | Cluster analysis for gene expression data: a survey[END_REF]. Reviews and comparisons of different clustering methods for gene expression data may be found in [START_REF] Datta | Comparisons and validation of statistical clustering techniques for microarray gene expression data[END_REF].

In practice, annotation databases are often used to perform a posteriori validation and interpretation of co-expressed gene clusters through tests of functional enrichment [START_REF] Steuer | Validation and functional annotation of expression-based clusters based on gene ontology[END_REF]. Such functional annotation may instead be directly integrated into the clustering model itself. For example, [START_REF] Tari | Fuzzy c-means clustering with prior biological knowledge[END_REF] incorporate GO annotations as prior knowledge in a fuzzy c-means clustering. [START_REF] Verbanck | A new unsupervised gene clustering algorithm based on the integration of biological knowledge into expression data[END_REF] proposed a clustering approach based on a distance defined conjointly on the similarity among expression profiles and that among functional profiles. [START_REF] Pan | Incorporating gene functions as priors in model-based clustering of microarray gene expression data[END_REF] and [START_REF] Huang | Combining gene annotations and gene expression data in modelbased clustering: weighted method[END_REF] proposed including gene annotation as prior information in a stratified mixture model. However, the inclusion of gene annotation directly in the model itself in this way may be questionable, particularly when they are also used to validate the gene clusters a posteriori. Moreover, as gene annotations tend to be incomplete, biases may be introduced if they are directly incorporated in the model, as unannotated genes (which represent those known to be unassociated with a given function as well as those of unknown function) may be erroneously separated from annotated genes.

One alternative to such approaches is to define a clustering model that accounts for external gene annotations without directly including them in the model itself. To this end model-based clustering provides a convenient framework, as it 1) allows for a large set of clustering models to be fit to the gene expression alone, and 2) facilitates the choice among this set a parsimonious model that simultaneously provides a good fit to the data and coherence with the external gene annotations. In this work, we address these points by proposing a model selection criterion that accounts for external gene annotations.

The rest of this paper is organised as follows. In Section 2, we present the context of model-based clustering and review classic model selection criteria. Our proposed annotated model selection criterion is presented in Section 3, and numerical illustrations of its behavior are presented on simulated data in Section 4 using Gaussian mixture models. Finally, we illustrate a co-expression analysis of real RNA-seq data in Section 5, and a discussion ends the paper.

Model-based clustering and model selection

Let y be the (n × q) matrix of observed gene expression, where n is the number of genes and q the number of biological samples. The vector y i denotes the expression of gene i (i = 1, . . . , n) across the q samples. In the context of model-based clustering, the data y are assumed to be sampled from a finite mixture density of K random variables, each with parameterized density φ (y i ; a k ), k = 1, . . . , K, where the mixture parameters (a 1 , . . . , a K ) are all assumed to be distinct. The density of y may thus be written as

f (y; K, θ K ) = n ∏ i=1 K ∑ k=1 p k φ (y i ; a k ), (1)
where θ K = (p 1 , . . . , p K-1 , a 1 , . . . , a K ) are the parameters of the mixture model, and (p 1 , . . . , p K ) are the mixing proportions with p k ∈ (0, 1) for all k, ∑ K k=1 p k = 1. For parameter estimation, the mixture model in Equation ( 1) may be thought of as an incomplete data structure model where z is the (n × K) matrix of unknown mixture labels, where z ik = 1 if gene i is from group k and 0 otherwise. Note that this matrix defines a partition of the genes.

Using the mixture labels z, the completed density of y may be written as follows:

f (y; K, θ K ) = n ∏ i=1 K ∏ k=1 (p k φ (y i ; a k )) z ki . (2)
The maximum likelihood estimate θK of the mixture parameters is computed through the Expectation-Maximization algorithm [START_REF] Dempster | Maximum likelihood from incomplete data via the EM algorithm[END_REF] by replacing the unknown labels z in Equation ( 2) with ẑ, defined as:

ẑik = 1 if arg max ℓ τ iℓ ( θK ) = k 0 otherwise,
where τ iℓ ( θK ) denotes the conditional probability given y i of the ℓth mixture component under θK :

τ iℓ ( θK ) = pℓ φ (y i ; âℓ ) ∑ K t=1 pt φ (y i ; ât ) .
In the context of model-based clustering, one important task is the choice of an appropriate model, most notably the revelant number of clusters K. To this end, a standard model selection criterion is the Bayesian Information Criterion (BIC) [START_REF] Schwarz | Estimating the Dimension of a Model[END_REF]:

BIC(K) = log f (y; K, θK ) - ν K 2 log(n),
where θK is the maximum likelihood estimator of the mixture parameters and ν K the number of free pa- rameters in the model with K components. This criterion is an asymptotic approximation of the logarithm of the integrated likelihood:

f (y; K) = θ K f (y; K, θ K )π(θ K )dθ K ,
where π(θ K ) is a weakly informative prior distribution on θ K . An alternative to the BIC is the Integrated Completed Likelihood (ICL) criterion [START_REF] Biernacki | Assessing a mixture model for clustering with the integrated completed likelihood[END_REF]:

ICL(K) = BIC(K) -Ent(K), (3)
where Ent(K) is the estimated mean clustering entropy

Ent(K) = - n ∑ i=1 K ∑ k=1 τ ik ( θK ) log τ ik ( θK ) ≥ 0. ( 4
)
Inria Note that the ICL is a BIC-like approximation of the logarithm of the completed integrated likelihood:

f (y, z; K) = θ K f (y, z; K, θ K )π(θ K )dθ K .
Because of the additional entropy term defined in Equation ( 4), the ICL favors models that lead to data partitions with the greatest evidence in terms of classification.

More recently, [START_REF] Baudry | Enhancing the selection of a model-based clustering with external categorical variables[END_REF] proposed an ICL-like criterion that takes advantage of the potential explicative ability of external categorical variables u = (u 1 , . . . , u R ) where u r iℓ = 1 indicates that the gene i is in category ℓ for the r th external categorical variable and 0 otherwise. The idea is to choose a classification z based on y that is coherent with u. Assuming that y and u are conditionally independent given z, the Supported Integrated Completed Likelihood (SICL) criterion is an asymptotic approximation of the logarithm of the integrated completed likelihood:

f (y, u, z; K) = f (y, u, z; K, θ K )π(θ K )dθ K .
The SICL criterion is defined as follows:

SICL(K) = ICL(K) + R ∑ r=1 U r ∑ ℓ=1 K ∑ k=1 n r kℓ log n r kℓ n k• , (5)
where U r is the number of levels of the variable u r , n r kℓ = card i : z ik = 1 and u r iℓ = 1 ,

and n k. = ∑ U r
ℓ=1 n r kℓ . The last additional term in Equation ( 5) quantifies the strength of the link between the categorical variables u and the classification z.

Taking genome annotations into account

As previously stated, the objective of this work is to make use of external gene annotations to choose a model for which clusters may be meaningfully interpreted both with respect to their expression profiles and their functional properties. To do so, we propose a novel model selection criterion that highlights the association between the clusters of expression profiles and the functional annotations associated with a subset of genes. Since gene annotations are binary variables (i.e., a gene is either annotated or unannotated), it may seem natural to directly use the SICL defined in Equation ( 5). However, in contrast to the situation considered by [START_REF] Baudry | Enhancing the selection of a model-based clustering with external categorical variables[END_REF], gene annotation information is often incomplete. More precisely, for each of the G annotation terms, indexed by g, the available information u g is as follows:

u g i =
1 if gene i is known to be implicated in function g, 0 if gene i is not known to be implicated in function g.

Note that u g i = 0 can indicate that information is missing (i.e., gene i has not yet been identified for annotation g) or that gene i is known to be unrelated to annotation g. As such, u g i = 0 does not represent the null level of variable and thus represents an incomplete binary variable. For this reason, the SICL criterion is not an appropriate measure of the link between an external annotation u g and a classification z, and a specific criterion must be defined to incorporate the gene annotation information into the model selection step. To this end, we propose the Integrated Completed Annotated Likelihood (ICAL) criterion as follows.

For each gene annotation u g , we first define the random matrix b g of latent variables indicating the allocation of the annotations among the K clusters:

b g ik = 1 with probability p g k if u g i = 1, 0 if u g i = 0. ( 6
)
Each row of the matrix b g is a random vector following a multinomial distribution with parameters u g i and (p g 1 , . . . , p g K ) if u g i > 0, and is the null vector 0 if u g i = 0. For the sake of simplicity, we first derive ICAL when a single external annotation b 1 is available. ICAL aims to select the clustering model that maximises the logarithm of the integrated annotated likelihood:

f (y, z, b 1 ; K) = θ K f (y, z, b 1 ; K, θ K )π(θ K )dθ K . ( 7
)
As for the definition of the SICL, the variables y and b 1 are assumed to be conditionally independent given z. Using Bayes formula, we have

f (y, z, b 1 ; K, θ K ) = f (y, z; K, θ K ) f (b 1 | y, z; K, θ K ).
Note that since y and b 1 are assumed to be independent given z, the conditional distribution of b 1 given z does not depend on y or the mixture parameters. Thus, as

f (b 1 | y, z; K, θ K ) = f (b 1 | z; K), it follows that: log f (y, z, b 1 ; K) = log f (b 1 | z; K) + log θ K f (y, z; K, θ K )π(θ K )dθ K . (8)
The last term in Equation ( 8) can be approximated with ICL(K) from Equation (3), and the first term may be approximated with

log f (b 1 | ẑ; K) = K ∑ k=1 n 1 k log n 1 k n 1 ,
where n 1 = card{i : u 1 i = 1} and n 1 k = card{i : ẑik = 1 and u 1 i = 1}. Finally, an asymptotic approximation of the expression in (7) leads to the Integrated Completed Annotated Likelihood (ICAL) criterion:

ICAL(K) = ICL(K) + K ∑ k=1 n 1 k log n 1 k n 1 .
The generalization of this criterion to the case where G > 1 gene annotations are available is straightforward. The aim is now to maximize the logarithm of the integrated annotated likelihood:

log f (y, z, b 1 , . . . , b G ; K) = log θ K f (y, z, b 1 , . . . , b G ; K, θ K )π(θ K )dθ K .
Assuming that b 1 , . . . , b G and y are conditionally independent given z, we have

log f (y, z, b 1 , . . . , b G ; K) = log f (b 1 , . . . , b G ; z, K) + log θ K f (y, z; K, θ K )π(θ K )dθ K .
Assuming in addition that b 1 , . . . , b G are independent and that gene annotations are missing at random, we can write

f (b 1 , . . . , b G ; z, K) = G ∏ g=1 f (b g |z, K), (9)
leading to the generalized ICAL criterion:

ICAL(K) = ICL(K) + G ∑ g=1 K ∑ k=1 n g k log n g k n g . ( 10
)

Inria

Comparing ICAL and SICL If we ignore the uncertainty associated with u g i = 0 (i.e., that gene i could either be unassociated with function g or that this information is missing), the SICL criterion could be considered to choose the model dimension K. In this case, using the notation from Section 2 and defining n k the size of the cluster k , the SICL may be written as follows:

SICL(K) = ICL(K) + pen SICL , where pen SICL = G ∑ g=1 K ∑ k=1 n g k1 log n g k1 n g k. + G ∑ g=1 K ∑ k=1 n g k0 log n g k0 n g k. , = G ∑ g=1 K ∑ k=1 n g k1 log n g k1 + G ∑ g=1 K ∑ k=1 n g k0 log n g k0 -G K ∑ k=1 n k log n k .
On the other hand, using the notation from Section 2 and defining n g

.1 = ∑ K k=1 n g k1
, the ICAL may be written as follows:

ICAL(K) = ICL(K) + pen ICAL ,
where

pen ICAL = G ∑ g=1 K ∑ k=1 n g k1 log n g k1 n g .1 , = G ∑ g=1 K ∑ k=1 n g k1 log n g k1 - G ∑ g=1 n g .1 log n g .1 .
We note that the last term in the equation above is a constant independent of K. Finally, we can rewrite ICAL as a function of SICL:

ICAL(K) = SICL(K) - G ∑ g=1 K ∑ k=1 n g k0 log n g k0 + G K ∑ k=1 n k log n k + constant. ( 11
)
From Equation (11), we note that the SICL takes into account both modalities (0 and 1) of the external variables u, while the ICAL discards the null modality (the -∑ G g=1 ∑ K k=1 n g k0 log n g k0 term). Moreover, it can be seen that the ICAL penalises a large number of clusters, while the SICL does not (the G ∑ K k=1 n k log n k term). As such, the ICAL tends to select parsimonious models with a relatively small number of clusters, as compared to SICL.

It is also helpful to consider the behavior of the ICAL and SICL criteria in extreme conditions. If the number of clusters K equals 1, the ICAL penalty pen ICAL equals zero whereas SICL penalty pen SICL is not null (∑ G g=1 n g 1 log

n g 1 n + ∑ G g=1 n g 0 log n g 0 n ).
In contrast, if the number of clusters K is equal to the number of observations, with one gene per cluster, the SICL penalty pen SICL equals zero whereas the ICAL penalty is not null (∑ G g=1 n g 1 log n g 1 ). In general, ICAL tends to merge clusters to group genes annotated for the same function, reducing the number of optimal clusters K with respect to the optimal number of clusters selected by ICL. SICL tends to split clusters in order to obtain clusters made up only of annotated genes, increasing the number of optimal clusters with respect to the optimal number of clusters selected by ICL. In other words, SICL tends to select more complex models than ICL while ICAL tends to favor more parsimonious models than ICL. Note that this behavior of ICAL and SICL are general trends, not rules: ICAL does not always merge clusters and SICL does not always split them since clusters for different solutions are not necessarily nested in each other.

Numerical illustrations

Simulation settings

To illustrate the behavior of the proposed ICAL criterion, we consider a numerical example. We simulate 200 observations from a mixture of four bivariate Gaussian distributions, 100 independent times (see parameters in Table 1). For a given model indexed by K, the estimation of parameters is performed with the R package Rmixmod [START_REF] Biernacki | Model-based cluster analysis and discriminant analysis with the MIXMOD software[END_REF][START_REF] Lebret | Rmixmod: The R Package of the Model-Based Unsupervised, Supervised and Semi-Supervised Classification Mixmod Library[END_REF] for a Gaussian mixture model with diagonal variance matrix (that is, the p k L k B k model in the notation of the Rmixmod package, corresponding to clusters with variable proportions, variable volumes, variable shapes and vertical or horizontal orientation). We estimate the parameters for models with the number of clusters K varying from 1 to 10 and perform model selection to select the most appropriate number of clusters. Over the 100 replicated datasets, the BIC most frequently selects four clusters (81 times). Indeed, we note that these clusters correspond to the simulated Gaussian components. The ICL criterion selects either three (54 times) or four clusters (46 times), as it tends to merge the two similar components (1 and 2 from Table 1) .

Component Mixing proportions

Component distribution 1 0.25 N 0 0 , 1 0 0 1.7 2 0.25 N 0 5 , 1 0 0 1.7 3 0.25 N 9 8 , 0.1 0 0 1 4 0.25 N 9 0 , 1 0 0 0.8
Table 1: Parameters of simulated datasets: the first two components are close to one another while the third and fourth are clearly distinct from the first two and also distinct from each other.

We illustrate the potential utility of accounting for external gene annotations in model selection by simulating such annotations and performing model selection with the corresponding SICL and the ICAL criteria. We simulate three types of functional annotations: u A , u B and u C (see Figure 1). The genes annotated for the first function u A are shared by the two closest mixture components (components 1 and 2 from Table 1). This annotation is designed to be associated to the components in the sense that it suggests the interest of merging the two clusters, as they share similar joint distributions and external annotations. The genes annotated for the second function u B are shared only by the two clearly distinct components (components 3 and 4 from Table 1). This annotation is designed to be unassociated with the components: although the components share a similar function, their joint distributions are too distinct to be merged from a modelling point of view. Finally, the genes annotated for the third function u C are randomly spread over the four components: meaning the annotation is mixed (half associated / half unassociated). For each function, we simulate the annotation using binomial random variables, with parameters fixed to yield on average 20 annotated genes over 200 possible genes.

Simulation results

All penalized criteria (BIC, ICL, SICL and ICAL) versus the number of clusters for one simulated dataset are displayed in Figure 2 (left). We note that the peak of ICAL is sharper for the three cluster solution than the peak of ICL. Over the 100 simulated datasets, ICAL selects three clusters 87 times, merging the two closest components 1 and 2 (Table 2). This three cluster solution is meaningful with respect to the Inria information provided by u A , as all annotated genes are attributed to the same cluster. In this case, the external information provided by the associated annotation u A reinforces the model selection. Using the same pattern as u A (annotations shared by components 1 and 2 only), we simulate twelve independent associated annotations using binomial random variables, each with parameters fixed to have on average 20 annotated genes over 200 possible genes. For this set of external annotations, the peak of the ICAL displayed in Figure 2 (right) is much sharper than the peak of ICL. Over the 100 simulated datasets, ICAL systematically selects a three cluster solution (Table 2). In contrast, SICL more frequently selects a fouror even five-cluster solution, as it leads to a preference of smaller clusters containing only annotated genes (i.e., a high specificity of annotation within each cluster). This demonstrates the utility of the ICAL criterion over the SICL, as it does not correctly take into account the specificity of gene annotation.

For unassociated annotation u B , the behavior of the information criteria versus the number of clusters for one simulated dataset is displayed in Figure 3 (left). We note that the ICAL criterion behaves similarly to the ICL. Over the 100 simulated datasets, ICAL, as ICL, leads to some uncertainty as to whether a three cluster solution (53 times) or a four cluster solution (47 times) is best (Table 2). In this case, the annotation u B is not related to the components and has no impact on the resulting clustering, even if the number of annotations is increased to 12, each simulated with the same pattern as u B as displayed in Figure 3 (right).

Finally, for the mixed annotation u C , ICAL most frequently selects three clusters (79 times) or four clusters (21 times). Because the annotation u C is mixed, there is less evidence to merge the two clusters on the left than in the case of the informative annotation u A . Using the three types of annotations at the same time (u A , u B , u C ), the ICAL criterion almost systematically selects three clusters (Table 2).

The potential utility of accounting for external gene annotations in model selection is highlighted in the numerical results summarized in Table 2. First, these results illustrate that the SICL is not welladapted to account for gene annotations in model selection; at best SICL behaves like ICL and at worst, erroneously splits clusters that should be merged. However, if the external information is associated to the components, even partially so, the use of the ICAL criterion improves model selection in terms of functional interpretability. If the external information is unassociated to the components, the ICAL criterion simply behaves like the ICL. 1. The model most commonly selected for each criterion is highlighted in red.

5 RNA-seq data analysis 5.1 Presentation of the RNA-seq data and clustering settings [START_REF] Mach | Extensive expression differences along porcine small intestine evidenced by transcriptome sequencing[END_REF] analyzed transcriptome differences in the small intestine of healthy piglets to better understand their immune response. The expression of 24924 genes across 12 samples was measured using RNA-seq, corresponding to 3 different tissues (the duodenum, the jejunum and the ileum), each sequenced for 4 different healthy piglets. We performed a differential analysis using a negative binomial generalized linear model as implemented in the edgeR package version 3.4.2 [START_REF] Inria Robinson | edgeR: a Bioconductor package for differential expression analysis of digital gene expression data[END_REF]. We identified 4021 genes as differentially expressed among any of the tissues after controlling the false discovery rate (FDR) below the level 0.05 with the approach of [START_REF] Benjamini | Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing[END_REF]. For the following co-expression analysis, we restrict our attention to this set of differentially expressed genes.

Prior to the co-expression analysis, we applied the voom transformation to stabilize the markedly unequal variabilities typical of RNA-seq data [START_REF] Law | Voom: precision weights unlock linear model analysis tools for RNA-seq read counts[END_REF], where library size normalization factors were computed on the full set of genes. Subsequently, Gaussian mixture models were estimated for the transformed data using the Rmixmod package version 2.0.2 [START_REF] Biernacki | Model-based cluster analysis and discriminant analysis with the MIXMOD software[END_REF] for a number of clusters from 1 to 50. For each model, we used a small EM strategy for initiation and repeated estimation 10 times.

Presentation of functional annotation data

The Molecular Signatures Database [START_REF] Liberzon | Molecular signatures database (MSigDB) 3.0[END_REF] was built by the Brain Institute and provides collections of annotated gene sets for use with the Gene Set Enrichment Analysis software [START_REF] Subramanian | Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles[END_REF]. The Molecular Signatures Database (MSigDB) contains collections of gene sets from several sources: positional gene sets, curated gene sets from online pathway databases, motif gene sets, computational gene sets, GO gene sets, oncogenic canonical pathways and immunologic signatures. We used the Canonical Pathways (CP) gene sets collection, compiling 1320 canonical representations of biological processes curated by domain experts from online metabolic and signaling pathways databases such as the KEGG (http://www.genome.jp/kegg), BioCarta (http://www.biocarta.com) and Reactome databases (http://www.reactome.org).

Among the 1320 CP in the database, 1131 are represented among the 4021 differentially expressed genes. We select the CPs for which annotated genes are overrepresented in the set of differentially expressed genes with respect to the set of non-null genes using a Fisher's exact test. Since a test is performed for every possible annotation (i.e., each CP), we select those whose adjusted p-value is less than 0.05, after applying a Bonferroni correction for multiple testing. This procedure yields 10 CPs of interest, as described in Table 3.

Model selection

We compare the results of model selection performed by the four different criteria presented in Sections 2 and 3: BIC selects 28 clusters, ICL and SICL select 23 clusters while ICAL selects 20 (see Figure 4).

The approximate correspondences between clusters in the ICAL and ICL solutions are displayed in Table 4. Although the result of the former is not perfectly nested in the latter, in many cases the attribution of genes to clusters in the ICAL solution is a result of collapsing or partially collapsing several clusters from the ICL solution. This suggests that the ICL favors a slightly more complex solution, as expected; we next investigate whether the more parsimonious solution of the ICAL appears to be coherent given the set of CP used.

For the ICL and ICAL solutions, we examine associations between clusters and CP using Fisher's exact test. Significant p-values are summarized in Table 5. The ICAL criterion yields a clustering that maximizes the number of genes annotated in each cluster for each CP while still only grouping genes that share sufficiently similar expression profiles. For example, we note that CP8 is associated with two different clusters in the ICL solution, while it is associated with a single cluster in the ICAL solution; similarly, CP10 is associated with three clusters in the ICL solution and only two clusters in the ICAL solution. On the other hand, although clusters 10 and 17 in the ICAL solution both share annotations for CP10, these clusters are not collapsed into one using the proposed criterion, as their expression dynamics are too different. As such, the ICAL solution appears to enable the identification of more biologically interpretable clusters than the ICL, while still ensuring that the clustered genes share sufficiently similar expression dynamics. Finally, we note that the ICAL solution exhibits two clusters of particular interest with respect to the biological processes studied: Cluster 5 (379 genes) is associated with CP3 (reactome homeostasis, p=0.0002) and CP8 (KEGG ECM receptor interaction, p=0.00001). Cluster 10 (297 genes) is associated with CP1 (reactome metabolism of lipids and lipoproteins, p=0.002), CP6 (reactome fatty acid triacylglycerol and ketone body metabolism, p=0.005) and CP10 (KEGG peroxisome, p=0.0001), all of which correspond to fatty acid metabolism. Both clusters 5 and 10 contain unknown genes that may be good candidates for follow-up studies to determine whether they may be implicated in the corresponding canonical pathways. b, c andd) versus the number of clusters for the pig RNA-seq data for 10 independent initializations, represented by 10 grey circles for each number of clusters K. Solid lines link the maximum of the criteria over the 10 initializations over the collection of models. The red crosses correspond to the maximum of the criteria, which correspond to the selected models.

Inria

ICAL clusters ICL clusters

Discussion

In this paper, we present a novel way to incorporate functional annotations into model-based clustering of gene expression data. To this end, we develop a model selection criterion, the Integrated Completed Annotated Likelihood (ICAL) which is designed to select the model that jointly maximises the goodnessof-fit to the data and the association of clusters and annotations. From a biological point of view, the ICAL criterion aims to select models with more interpretable clusters than those selected by BIC or ICL.

It is important to note that the functional annotations are not directly included in the clustering model and are only used to select the best model. This approach is a good compromise between two opposite strategies: including functional annotations directly in the clustering model [START_REF] Morlini | A latent variables approach for clustering mixed binary and continuous variables within a Gaussian mixture model[END_REF] or excluding them altogether and using them only to validate clusters a posteriori. Since we do not include annotations in the clustering model, we detect associations between annotations and clusters with a stronger evidence than if we had included the external annotations in the clustering model. In particular, the ICAL criterion is a good way to include prior biological expertise without according it too much importance, which is a good balance between what can be observed in the data and what experts expect to see in the data.

As illustrated in numerical simulations, the performance of the ICAL is highly dependent on the quality of the information provided. Selecting the appropriate annotations to include in model selection is an important step and should be performed by an expert. We also suggest the use of gene annotation databases that are curated manually by experts, such as the gene sets collection from the MSigDB database [START_REF] Liberzon | Molecular signatures database (MSigDB) 3.0[END_REF].

In this work, we applied the ICAL using the framework of Gaussian mixture models, but the extension to other mixture models is straightforward; including Poisson [START_REF] Rau | Co-expression analysis of high-throughput transcriptome sequencing data with Poisson mixture models[END_REF] or Dirichlet multinomial mixture models [START_REF] Holmes | Dirichlet multinomial mixtures: generative models for microbial metagenomics[END_REF]. In addition, this model selection strategy may be useful for other types of data which may also be associated with incomplete external annotations (e.g., sociology, marketing).

Figure 1 :

 1 Figure1: Illustration of a simulated dataset and three annotation patterns. For each figure, the 200 observations are drawn from a mixture of Gaussian bivariate components whose parameters are defined in Table1: circles, triangles, inverted triangles and diamonds correspond to components 1, 2, 3 and 4. The three figures correspond to three annotation patterns: associated annotation u A (left), unassociated annotation u B (center) and mixed annotations u C (right). For each annotation, the 20 annotated genes are represented by coloured bold crosses.

Figure 2 :

 2 Figure 2: BIC, ICL, SICL and ICAL information criteria versus the number of clusters on one simulated dataset for the informative annotations: u A (left) and u 1 A , . . . , u 12 A (right). Triangles indicate the maximum value attained by each criterion.

Figure 3 :

 3 Figure 3: BIC, ICL, SICL and ICAL information criteria versus the number of clusters on one simulated dataset for the non informative annotations: u B (left) and u 1 B , . . . , u 12 B (right). Triangles indicate the maximum value attained by each criterion.

Figure 4 :

 4 Figure 4: BIC, ICL, SICL and ICAL information criteria (respectively a, b,c and d) versus the number of clusters for the pig RNA-seq data for 10 independent initializations, represented by 10 grey circles for each number of clusters K. Solid lines link the maximum of the criteria over the 10 initializations over the collection of models. The red crosses correspond to the maximum of the criteria, which correspond to the selected models.

Table 2 :

 2 ). Triangles indicate the maximum value attained by each criterion. Number of simulated datasets for which each model (K = 1, . . . , 10) was selected by BIC, ICL, SICL and ICAL for several external annotations over 100 independent datasets simulated with parameters detailed in Table

	Inria

Table 3 :

 3 Number of genes annotated for each canonical pathway (CP): among the 4021 differentially expressed (DE) genes and among the full CP gene set collection of the MSigDB database.

	Inria

Table 4 :

 4 Approximate composition of the 20 clusters of the ICAL solution with respect to the 23 clusters of the ICL solution. Lines in bold correspond to clusters of the ICAL solution that are formed by several clusters or parts from clusters of the ICL solution. For example, Cluster 5 of the ICAL solution is approximately made of Clusters 12 and parts of Clusters 5, 20 and 22 of the ICL solution.

	Cluster 1 1 2 9 Cluster 2 15
	Cluster 3	10
	Cluster 4 Cluster 5 1 11 2 5 + Cluster 6 2 + Cluster 7 8	12 1 2 5	+ 1 2 20 + 1 2 22 + 1 3 18
	Cluster 8 Cluster 9 Cluster 10 Cluster 11 Cluster 12 Cluster 13 Cluster 14	4 3 7 13 + 1 + + + 4 20 + 1 9 + 16 1 2 6 1 2 6 2 22 23 7 + 17 + 1 3 18 21
	Cluster 15	19
	Cluster 16 Cluster 17 Cluster 18 Cluster 19 1 14 + 1 1 3 18 1 4 20 + 1 2 5 Cluster 20 16

Table 5 :

 5 Table of associations between clusters and CP for the ICL solution (a) and the ICAL solution (b). Associations are detected using Fisher's exact tests: the number of stars indicates the value of the p-value (⋆ below 0.01, ⋆⋆ below 0.001, ⋆⋆⋆ below 0.0001).

	Inria

RR n°??

rue Honoré d'Estienne d'Orves Bâtiment Alan Turing Campus de l'École Polytechnique 91120 Palaiseau Publisher Inria Domaine de Voluceau -Rocquencourt BP 105 -78153 Le Chesnay Cedex inria.fr ISSN 0249-6399

Acknowledgements

We thank Jordi Estellé for providing the RNA-seq data in section 5 and giving insights on the external annotations and clustering results.


Joachim Schöpfel
email: joachim.schopfel@univ-lille3.fr.páginaen

Keywords: academic libraries, future, new contents, information value chain Resumen bibliotecas académicas, futuro, nuevos contenidos, cadena de valor de la información

This article discusses various aspects of the history and survival of libraries, thanks to their adaptability, diversity and variability as well as their future viewed from the past due to: the rapid growth of content, development of new services increasingly oriented to the user, impressive technological changes, creation of new job profiles, virtualization of their user communities, content production and globalization. It also shows the existence of several futures based on a swot analysis and changes in key functions such as acquisitions, gateways to information and its preservation, some positive and negative points that depend largely on the academic institutions they serve, management of new content (in particular the impact of the Internet, the preservation of heritage material and data management), its new involvement in the information value chain (such as hosting and management of repositories, knowledge management, evaluation of research and text and data mining) among others. It concludes with several important questions that need to be addressed to reach some conclusions of their possible future.

BIBL. UNIV., ENERO -JUNIO 2014 VOL. 17, No. 1

The Future of Academic Libraries On history and survival T he Danish Nobel prize-winner Niels Bohr once said: "prediction is very difficult, especially about the future". His quotation should remind us, in times of Mayan calendar prophecies, to be cautious with easy predictions, be they about the end of the world, about the winner of the 2014 Brazil World Cup, or about the future of academic libraries. Nobody can tell with confidence what the future will be made of, for the simple reason that nobody has been there before. But even without reading in the coffee grounds or from the Tarot cards, we can make a guess about what the future could, or should be.

The first thing we can say with certitude is that libraries look back on a long history. As this paper is not about the past but about the future, it may be enough to remember that since the ancient libraries of Ashurbanipal, Alexandria or Pergamum, the concept of library as a cultural institution has survived many political, economic, cultural and technological revolutions and other disasters. In particular, they have survived the Gutenberg press and more recently, informatics and the personal computer. Today, it seems that the Gutenberg galaxy has come to an end and that new information technologies and behaviours, such as mobiles, cloud computing and digital nomads will challenge libraries. In this fast moving environment, what will be the future of academic libraries? Will they survive? Now, in natural and human history the survivor is not necessarily the fittest and strongest type or species but the one who adapts best. Dinosaurs were not worse on future prediction than insects but adapted less well. So, my preliminary remark would be that if academic libraries survive in the 21st century, the reason will not be that they represent the very best and finest and definitive model of scientific communication but because they are flexible and able to take on the colours of their environment, just like chameleons. The velocity of academic libraries that invaded the Web 2.0 landscape and adopted its paradigms is a recent example for this great capacity of adaptation.

Another argument in favour of their survival is their amazing diversity and variability. Variability is essential to survival, especially in unstable and fast-changing environments. Even if today we don't know which model will survive, the high-tech learning centre, the digital library in the clouds, the small and highly specialised research library, or the library guardian of heritage collections, we can be confident that at least some of them will still be there in twenty, thirty or even fifty years, offering as before (but not the same) high quality services to their patrons and communities. Also, we can be sure that academic libraries will have by then generated new models and initiatives, and that conferences like icul at unam will certainly discuss case studies and experiments that we cannot imagine today.

For our purpose this means that even if prediction about the future may be rather difficult, academic libraries have shown in the past and until today their adaptability and variability and this will probably be the best guarantee and key for survival. First of all, experts were conscious about the rapid growth of content. More and more items were expected to be published and disseminated, and these items were expected to be more and more different, in terms of support, format and typology. The impact on libraries was anticipated in two different ways: an increasing workload for the processing of these items, and the shift of the core activity from the book to information and knowledge, i.e. increasing added value for the end user.

Another relevant prediction was about the development of new, quality services, with the focus moving from traditional goals and missions to the information needs and practices of the end user and the community. The third and perhaps most simple prediction was that the major changes would be technology-driven. In other words, libraries were seen as being in need of adaptation, not as a driving force or "spearhead" but more so as "victims" of new technology and running a double risk of being unable to keep pace with progress and customers' needs, and losing their soul.

The fourth main element of prediction concerned the need for change of management and the development of new job skills and profiles, such as the new job of the digital librarian. However, other issues were rather weak signals, on the edge or even outside of the field of prediction. We can cite at least three less anticipated developments, at least before they were at the door of the libraries:

1. Virtualization of community: the desertion of reading rooms, the "remote" use of library services, and in particular the library 2.0 concept. 2. Content production: the changing value chain of scientific communication, where the academic libraries will move from acquisition and conservation to production and publishing of content. 3. Globalization: the libraries' role in the society, and the impact of the major challenge of society, i.e. sustainable development, on the marketing, management and functioning of libraries.

Of course, it is easy to criticize the accuracy of past predictions. As a general rule, new generations always know better than the older. Probably, our generation will not be better at predicting the future than they were. But where are we now? What can we say about our own future, about the future of academic libraries, from our viewpoint and experience as lis professionals and scientific users?

Not one but many futures

In fact, speaking about the future of academic libraries may be improper and misleading in so far as there probably is not one but many futures, because of the great adaptability and variability of the concept. One size does not fit all, and variability is a key for survival, as already mentioned above, especially in a complex and dynamic environment.

It may be helpful to summarize from literature 2 and experience some factors that will foster or hinder the development of academic libraries. Figure 3 presents some of these factors as a swot grid. Of course, figure 3 is all but exhaustive or complete and will not replace an in-depth strategic analysis of academic libraries. Nevertheless, it helps to show some perspectives for development and, also, different aspects libraries should deal with carefully and with caution.

• Strengths: Apart from their adaptability, their excellent knowledge of the information behaviours and needs of the scientific communities is a key element for future development. Other positive factors are their physical space that can become an asset for the development of new services (see below), and their long tradition with networking and exchange on experiences and projects. • Weaknesses: Too much focussing on collections may not be useful when it comes to adopting a user-and community-centred approach. Sometimes, academic libraries, in spite of their excellent knowledge of their communities appear rather isolated, with weak marketing and low image. Even with a public mission of culture, education and research, academic libraries should not forget that they need more than ever successful lobbying and marketing in order to develop their service offer. • Opportunities: All new developments of the campus and in the scientific environment are opportunities and options for the future. a "gateway" or starting point for locating information. 3 Yet, who will manage the digital rights for those items protected by intellectual property? Who will provide access to "hidden" material that is not disseminated on Internet? • Preservation: Acquisition and subscription to documents are substituted with temporary access to online resources. Who will guarantee long-term conservation and availability of these resources? Who will preserve grey literature, data, and non-digital resources?

Given these challenges, academic libraries are in competition with other institutions and organisations, although they have some interesting assets and options that may co-determine their future.

For better and for worse

The future of the academic libraries is on the campus. It depends on the future of the university. Like an old couple, their fates are closely related, for better or for worse. The university's strategic decisions determine the library's degree of freedom. What is good for the university, its staff, scholars, students, scientists and partners, becomes a priority for the library. One cannot imagine the future of academic libraries without taking into account their immediate environment, their academic stakeholders, donors, content providers and customers on the campus.

First of all, this means that there cannot be one and only one model for academic libraries. Universities are different one from the other. Not all have Nobel laureates or Fields medallists among their staff or alumni, and the number of highly cited researchers, highly ranked papers and staff varies from campus to campus. Again, one size does not fit all. A research university does not produce and consume scientific information in the same way as a technological university or a state university with focus on education and learning. The aca-3 tenoPir, Carol. The Value Gap.

The rapid development of open access publishing and the dissemination of research data offer several opportunities for new services where the academic libraries can add value to scientific communication. Also, the digital divide and the need for information literacy, free and equal access to information, and for availability and uptake of information technology, is a challenge for academic libraries, especially in emerging and developing countries. • Threats: Even if changing environments always threaten the status quo of institutions, the actual risks for academic libraries appear to be budget cuts (and transfer of information funding to other structures), together with increasing disintermediation and lack of support by their scientific communities, which may be related to weak lobbying and marketing. This is the time to take a short break to remind ourselves of the main traditional functions of academic libraries, i.e. acquisition of documents (buyer), as a gateway to documents and preservation of these items. For a couple of years now, these functions have started to change:

• Acquisition: The part of scientific information that academic libraries (can) buy is continuously decreasing because of the exponential growth of scientific publications, because of Internet and open access, and because of limited budgets. Yet, who will guarantee quality, richness and variety of content and support, who will make selections and prevent information overload?

In other words, who will build collections in line with the needs of scientific communities? Will the acquisition function partly be made of author processing charges (acp)

for gold road open access journals? • Gateway: Because of powerful search engines, discovery tools, social networks etc., the library is seen less and less as demic libraries must provide information content and services in line with the specific needs and practices of their communities. Their main question must be: "What is my added value for education and research?" And the answer must be a specific value proposition, not a general or standard offer.

The second observation is that this value proposition must include more than information and documentation. Each university conducts its own policy with respect to society, culture, ecology and economy. Part of the campus, academic libraries are expected to contribute to these projects and actions. In particular, today the performance of a university is also measured in terms of the students' vocational integration. Do the students find work easily, or is it that the university generates unemployed people? For academic libraries, the question is not if they can yes or no help to reach this objective, but only how they can contribute, beyond education and research. 4 Third comment: in spite of all the differences, academic communities and institutions mostly share some common values and ethics, such as scientific freedom, integrity, excellence and humanism.

Handling new content

The holdings of academic libraries are extremely rich, covering the whole range of scientific production, monographs and journals, proceedings, theses and dissertations, working papers, project reports and unpublished material, and also photographs, maps, audiovisual material, manuscripts, letters, rare and precious old documents etc. The capacity to manage all these items and to make them available for the scientific communities is one of the strong points of the academic library staff, and there is no reason why this should change in the future.

Yet, we can identify at least three different developments that will increasingly challenge academic libraries from now on, i.e. openly available content on Internet, scientific and cultural heritage material, and research data.

Internet: More and more scientific content is freely available on Internet, through institutional repositories (green road) or open journals (gold road), via social networks, wikis, blogs, personal websites, etc. Together with the rapidly growing number of articles and books published and disseminated via the traditional channels of scientific communication, this situation bears the risk of information overload and moreover, because of partly lacking validation or labelling, of information pollution. The challenge for the academic libraries is twofold: provide discovery tools for effective and efficient item selection, and propose a selection in line with the needs of its scientific communities and with a quality guarantee. Both tasks are not really new for academic librarians. Yet, today they must (at least, partly) shift from acquisition policy to a kind of Web intelligence, and from catalogue and database production to the curation and tagging of web resources.

Heritage: Most academic libraries possess some kind of unique material, be it already in the public or not. Today, the scientific communities, also the governments, research organisations, and funding bodies want these often hidden materials to be uncovered and made available, as primary source for further research but also as witness and evidence of past research, culture BIBL. UNIV., ENERO -JUNIO 2014 VOL. 17, No. 1

Joachim Schöpfel

this content available to the researcher as end-user.

Compliant with the usual business model of commercial and learned society publishing, this position in the value chain has started to change with the introduction of new business models and forms of scientific communication.

The Dutch economist Hans Roosendaal and his colleagues have described how new technologies and information vectors push the institutions and organisations to experiment new business models, with different value chains unknown up to now. 10 In particular, they studied models where academic libraries move along the value chain, from selection and acquisition (downstream) to production and dissemination (upstream). As they put it: "the major organisation challenge will be to absorb the library into the research organisation (…) The main tasks of the library will continue to exist (while) new tasks will have to be developed, such as information creation and tasks related to required technical competence, new interfaces and new service providers".11

This new function will most often be related to the hosting and management of institutional repositories or other document servers. In this role, academic libraries will take over some of the publishers' traditional activities, such as handling intellectual property rights (together with legal advice), managing deposits (format control, versioning…).

Often, this editorial function will include some kind of selection and quality control; sometimes, this selection process may be separated from dissemination and appear "downstream", for instance as post-deposit peer review or other, alternative forms of commenting and tagging. Sometimes, too, the academic libraries will develop new services related not, as before, to their acquisition and gateway function, but to the production and dissemination of content, such as attribution of unique identifiers, web analytics and usage statistics with options for altmetrics, export and exploitation of publication files for scientometrics and evaluation, etc. and history. For academic libraries, the challenge here is to identify this material, to set up, fund and manage digitization projects, and to handle sometimes rather complex questions of intellectual property, digitization, metadata, platform, access rights and so on.

Data: Scientists and computer specialists have been announcing for a couple of years now the fourth paradigm of science, which means data-intensive scientific discovery and the possibility to disseminate scientific results without traditional publications. 7 Academic libraries face three challenges: collect and preserve these new digital objects on specific platforms, with a specific service environment; create and manage metadata and identifiers for all kinds of datasets; and connect datasets and publications. 8 Academic libraries have already begun to invest this new field. 9 However, as data are not just data, and stm are not like ss&h, it may be that in the future, the fourth challenge will be to handle both big and small data, i.e. data produced massively, in standard formats and by big scientific facilities or networks, together with small datasets produced by individual researchers, small research teams, heterogeneous by definition, such as datasets, av files and other material submitted together with phD theses in Social Sciences and Humanities.

Will the academic libraries be able to do the splits between traditional activities and new challenges? Will they be able to meet all challenges at the same time? Or will the complexity of the new tasks push academic libraries to more specialisation; so that some will curate datasets while others put the focus on digital libraries or discovery tools and web indexing?

Moving along the value chain

The traditional function of the academic library is selection and acquisition of content, at the end of the value chain of scientific information, with the objective to make 7

The Fourth Paradigm: Data-intensive scientific discovery.

Edited by Tony Hey, Stewart Tansley and Kristin Tolle.

8

Hey, Tony, Hey, Jessie. e-Science and its implications for the library community. 9

Brase, Jan, Farquhar, Adam. Access to Research Data.

We cannot, in a short communication, cite all examples where academic libraries move into new fields of action, with new functions and roles, and with new positions in the value chain of scientific information.12 What is important, yet, is to understand that these changes and this questioning of the traditional value chain is not a kind of flash in the pan but is meant to stay. Again, this new situation requires a capacity we already mentioned above: flexibility, adaptability, the capacity (and the motivation) to try and to experience. The future will surely not be a kind of "return to paradise" where all things are in their place, but rather a game with uncertainty and incitation to test.

I will finish with two particular developments, even if it may be too early to define the specific role of academic libraries. Nevertheless, it is obvious that they are not in their usual position in the traditional value chain.

The first development is knowledge management, a service complementary to (or in the place of) the management of books and journals. Academic libraries are interested in semantics, text and data mining, ontologies and so on. Will they be able to transform this interest in a genuine service offering?

The second development is the contribution of academic libraries to current research information systems (cris), i.e. evaluation and management of research.

How will they connect their data silos of records and full text? Will they do more than export records, identifiers, etc., to such cris?

My personal conviction is that to both questions, the future will give an affirmative answer. Yes, academic libraries will do text and data mining, and yes, they will be active partners of cris infrastructures. In both cases, they quit their usually attributed place in the value chain, from downstream to upstream, from acquisition to production, and in both cases, formerly peripheral and complementary services may become part of the core service offer.

A good place

Most often, academic libraries are not virtual or in the clouds but real places, buildings with a given number of more or less useful square metres. 13 On most campuses, a square metre is a rare and wanted item. Today, students and staff go to libraries less than before, and this puts libraries at risk. So why not redesign their physical space and create a good place where students and staff would love to go and spend time, even if they do not want to read books or journals?

In fact, more and more libraries have already created such space, based on the concept of learning centres.

In short, a learning centre is a building or rather, an innovative architecture that provides "a seamless network of services, libraries, information gathering, social spaces, spaces to study, restaurants, cafes and beautiful outdoor spaces".14

A place to work alone or in a group, to learn, read, surf, eat and drink, relax, or even do nothing. Yet, a place connected to the world, to others, to Internet and social networks, a resourceful place, with access to documents, hard-and software, assistance, help and advice. A "third place" compliant with Ray Oldenburg's description: welcoming and comfortable, highly accessible, free or inexpensive, with food and drink, and with regulars such as staff. 15 Make the academic libraries look like a Starbucks may not be realistic in all cases, yet one should keep the principle in mind: to provide a place that people will like on Facebook, a caring environment that they will BIBL. UNIV., ENERO -JUNIO 2014 VOL. 17, No. 1

Joachim Schöpfel tainable development at the heart of libraries and to adopt the international action plan called Agenda 21 as a framework for library research and development. 19 Sustainable development is on mankind's agenda. The United Nations action plan Agenda 21 is clear on one point. The solution cannot be found on the local level; though without local action, there will be no global solution. Twenty years after the Rio Earth summit, the mandate of the academic libraries should no longer be confined to traditional concerns about collection preservation or helpdesk assistance, but should also include a contribution to sustainable development. Thus, our proposal is to apply the Agenda 21 to library marketing and management, as a conceptual framework to evaluate, set goals and make decisions in libraries and information services. Not so much to reinvent libraries, but to rethink their way of working, their projects and objectives, in terms of sustainable development -this is the next challenge for library marketing and management.

Academic libraries are scientific and cultural institutions, supporting education and research, but there is more than that -they are also part of the local campus and, like any other service, potential contributors to the sustainable development of society and mankind, and should be evaluated within this framework. The Rio+20 United Nations Conference on Sustainable Development 2012, twenty years after the first Earth Summit, reminds us that "sustainable development emphasizes a holistic, equitable and far-sighted approach to decision-making at all levels. (...) It rests on integration and a balanced consideration of social, economic and environmental goals and objectives in both public and private decision-making. "20

Academic libraries are but a small piece on the global game field. Yet they are part of the game, and society needs their specific contribution for sustainable development. 21 The growing numbers of green academic support, where they will return because they know they will have a good time and find what they want. For libraries, this may also mean to welcome "non-optimal users", students that don't know how (or don't want) to behave like a usual library patron. Academic libraries will have to adapt to these new generations, and will be able to do so.

While speaking of useful space and third place, it may be interesting for the academic libraries to learn from other concepts, such as the community offices 16 that are to provide support to local initiatives and groups who work in a community development context (with mentoring and consultancy, training and capacity building, skills training, best practices etc.), or the coworking 17 that puts the focus on a shared working environment (office), shared values and the establishment of a co-working community. These, together with idea stores, information commons, etc., are social developments in the community that will be extremely interesting for academic libraries in the future, especially with respect to their social outreach and their contribution to the students' vocational success (see above).

In the heart of society

"Meeting the needs of the present without compromising the ability of future generations to meet their own needs" 18 -does sustainable development matter to libraries? Librarians may be committed to ecology and environment. Yet, the literature about the future of academic libraries most often deals with modern information and communication technologies, business models and society. That is not wrong, but it is not enough. Our proposal is to put the concept of sus- libraries show the way and may serve as models. Yet, sustainable development asks for more, and academic libraries will need to learn new concepts such as social responsibility, accountability and contingent valuation as frameworks for further evolution. 22 They have already started to move in this direction, with concepts such as the lifelong library with independent learning provision and knowledge flows "just in case" and "just in time". 23

Trying the smart library?

Our environment is becoming increasingly urbanized, and the city may be the future of mankind. Our highly urbanized and connected culture gave birth, a couple of years ago, to a new concept of urbanism, called the intelligent or smart city. 24 Smart city stands for a comprehensive framework of urban policy and governance, innovation and infrastructure, modern information and communication technologies and connectedness, economic competition and individual lifestyle, and sustainable development.

This mixture of different dimensions on information technologies, mobility, digital nomads, and local community makes the concept relevant for the discussion on the future of academic libraries. At least, the concept of the smart city may be helpful and stimulating to consider the functioning and future options of academic libraries from "outside", as a challenge for innovative concepts, based on local resources and history but at This, together with the mobilization of the community around such a project, must appear familiar to those, librarians or scientists, interested and engaged in the future of academic libraries. Perhaps it is still too early to develop a consistent concept of the smart academic library, a library that is social, open, digital, connected, mobile, networking, a virtual space and at the same time, a good place to live and to learn and to work. But I admit that among all options, this is the one that I prefer and moreover, that I think is the most likely. We should work on it.

Good for walking

Some topics mentioned above may be rather familiar to academic librarians, while others may appear less obvious and perhaps even unrealistic and utopian. But as Eduardo Galeano said a couple of years ago, utopia is good for walking even if it is not sure at all to reach her one-day. Information Science, 2011, vol. 43, no. 3, p. 146-156.

Figure 1 :

 1 Figure 1: Mayan calendar (source: http://www.historik.de)

Figure 2 :

 2 Figure 2: Word cloud of articles on the future of libraries. 1

Figure 3 :

 3 Figure 3: A strategic analysis of academic libraries (from top left to bottom right: strengths, weaknesses, opportunities and threats)

  library, connected, part of a grid, useful, innovative, creative, user-centred, and urban? It may not be easy to find time for the future, while struggling hard every day with budget cuts, it failures, overdue items, claims and invoices. Also, academic communities are not always really supportive and do not always understand the problems and projects of librarians; and new generations are what they are. Yet, as we all have been raised in some way or other with 20th century existential thinking, I would like to add that the struggle itself is enough to fill a man's (and a woman's) heart and that, adapting the famous quotation of Albert Camus, we therefore should imagine the academic librarian happy. a Postscript: Keep your critical mind. "Experts are often overconfident… Their failures reflect the basic unpredictability of the events they try to forecast… (and) some environments are worse than irregular". 27 27 kahneMan, Daniel. Thinking, Fast and Slow.

Figure 4 :

 4 Figure 4: Sisyphus (source: http://commons.wikimedia.org)

1

  The word cloud is extracted from Broady-Preston, Judith y cox, Andrew. The Public Library as Street Corner University: back to the future?; cuadra, Carlos A. The Local Electronic Library: science fiction or the real future?; dowler, Lawrence and Farwell, Laura. The Gateway: A Bridge to the Library of the Future; draBenstott, Jon, y otros. Designing Library Facilities for a High-Tech Future; Mcdevitt, Phillip. The Future Library; Morales, Estela. The Future of the Library: a view from Mexico; Murr, Lawrence E., williaMs, James B.

	The Roles of the Future Library; niels, Mara. Politics of the
	Library of the Future;

  Paton, William B. The Library of the Future; winzenried, Arthur, Miido, Helis. The Librarian and the Library User: what the future holds.

  25"If libraries did not exist, would someone invent them?"26 It may be that the good questions about the future of academic libraries are not what the future will be (no one really knows) or which options seem to be more likely than others, but if you and all of us take time for the future, and if we are able to set aside time to prepare the future, instead of (only and always) doing routine work, can you imagine life without Mozart? But what about life without libraries? Can you image science without a library? Would you be the one to invent libraries? What are your five selling points? What value does your library add to the academic campus, to education and research? Who are your "customers", why do they use your services? How do you think your library will develop in the next five years? How should it develop? Where are your models and examples that frame your decisions? Do you think global? And would you like to speak of your library 13

BIBL. UNIV., ENERO -JUNIO 2014 VOL. 17, No. 1

The Future of Academic Libraries

Changes in the Value Chain of Scientific Information: economic consequences for academic institutions. Hans E. Roosendaal, and Scientific Publishing: From Vanity to Strategy. Hans E. Roosendaal, y otros.

Scientific Publishing: From Vanity toStrategy, op. cit.,

See for instance the Library Publishing Coalition (LPC) with more than 50 local initiatives (October 2013): "Based on core library values, our mission is to foster collaboration, share knowledge and develop common practices, all in the service of publishing and distributing academic and scholarly works". <http://www.librarypublishing.org/>

See rizzo, Joseph C. Finding your Place in the Information Age Library.

Rolex Learning Center at Lausanne, Switzerland <http:// rolexlearningcenter.epfl.ch/page-34751-en.html>

oldenBurg, Ray. The Great Good Place: cafés, coffee shops, community centers, beauty parlors, general stores, bars, hangouts, and how they get you through the day.

schöPFel, Joachim, McKiernan, Gerry. Towards the Global Library -Applying the Agenda 21 to Library Marketing.

20 <http://www.uncsd2012.org/index.php?

menu=62>21 Jankowska, María Anna, MarcuM, James W. Sustainability Challenge for Academic Libraries: Planning for the Future.

galeano, Eduardo. Walking Words, p. 326

Batt, C. Library 2050, p. 400 The Future of Academic Libraries

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