Sarab Tay
email: sarab.tay@ifsttar.fr

Juliette Marais
email: juliette.marais@ifsttar.fr

Weighting models for GPS Pseudorange observations for land transportation in urban canyons

Keywords: GNSS signal propagation, urban canyons, multipath, state of reception, weighting models, carrier-to-noise ratio, elevation angle

This paper adresses the problem of position computation in an urban canyon, using signals transmitted by Global Navgation Satellite Systems (GNSS) satellites. Due to the high masking level of buildings in a dense urban environment, the signals arrive at the receiver antenna often by more than one path (multipath). Multipath is a source of positioning error, since the receiver solutions for position fail to converge, because of the travel time of the received signal and the moving vehicle. In this paper, we are presenting a post-processing treatments based on observations variances modelling, in order to solve for vehicle position in an urban canyon.

I. INTRODUCTION

Localization systems are part of the improvement and attractivity efforts for better collective transportation systems. GNSS signals are widely used because this localization solution does not require to enhance the number and thereby the cost of investment and infrastructure. However, localization service quality is strongly degraded in urban environments where the signals are highly affected by diverse types of obstacles located around the receiver antenna. Signals are then subject to multipaths which decrease the accuracy of positioning. Moreover the EGNOS services devoted to increase accuracy by transmitting complementary signals by geostationary satellites suffer here from masking phenomena which make them unavailable. One of the solutions is to reduce the degradations and improve accuracy, it is explored in the COSYS/LEOST team. It consists in estimating a priori the conditions of signal reception. In this paper, we will present some weighting models based on the GNSS received signals parameters, such as the satellite elevation and the signal strength in terms of the carrier to noise ratio (C/No), along with and the signals' state of reception in an urban canyon.

II. URBAN CANYON ENVIRONMENT

Four satellites at least are necessary to compute a GNSS position. A time of arrival is extracted from each received signal that corresponds to the satellite-to-receiver distance. As summarized in eq. 1, the pseudorange measurement is mainly affected by the propagation through the atmosphere and the environment arround antenna :

ρ s t,m = d s t -c(δt s -δt u ) + (I s t + T s t ) + t, (1)
where :

• d s t is the euclidian distance between the satellite s and the user at time t,

• δt s and δt u are respectively the offset between the GPS system time and the receiver clock, and the offset between the GPS system time and the receiver clock,

• I s t and T s t are the ionospheric and the tropospheric errors,

• t = m s t + w t are the observations errors, with m t is the error due to signal multipath, and w t is the receiver noise.

The ionospheric and tropospheric errors can be modeled such in [START_REF] Klobuchar | Ionospheric effects on gps[END_REF], whereas the poor satellite geometry and site environment antenna are difficult to treat. In urban canyons, the presence of buildings of different heights, structures, and materials, dense vegetation, and street elements reduces highly the number of visible satellites and increases the presence of multipath.

Received signals may be classified into three types:

• Line-of-sight (LOS) signals (direct),

• Non Line-of-sight (NLOS) signals (reflected),

• Blocked signals.

Several techniques have been developped for multipath mitigation, for instance the Narrow Spacing Correlator [START_REF] Dierendonck | Theory and performance of narrow correlator spacing in a gps receiver[END_REF], Multipath estimation Delay-Locked-Loop algorithm (MEDLL) [START_REF] Nee | Multipath estimating delay lock loop : approaching theoretical accuracy limits[END_REF], some Bayesian approaches [START_REF] Lentmaier | Bayesian time delay estimation of gnss signals in dynamic multipath environments[END_REF] and array antenna algorithms [START_REF] Konovaltsev | Performance assessment of antenna array algorithms for multipath and interference mitigation[END_REF]. Other solutions such as in [START_REF] Attia | Segmentation d'images par combinaison adaptative couleur/texture et classification de pixels. application à la caractérisation de l'environnement de réception des signaux gnss[END_REF] and [START_REF] Peyraud | About non-line-of-sight satellite detection and exclusion in a 3-d map aided localization algorithm[END_REF] are made to exlcude all the NLOS received signals. However, in [START_REF] Attia | Segmentation d'images par combinaison adaptative couleur/texture et classification de pixels. application à la caractérisation de l'environnement de réception des signaux gnss[END_REF] it was proved that a simple exclusion decreases the accuracy of user position in an urban area.

III. OBSERVATION WEIGHTING MODELS

In order to improve user position computation accuracy, we are using all received signals, jointly with the information on the state of reception. Concretly, we propose a weighting model depending on the quality of the signals and the geometrical form of the surrounding antenna environment. The strength quality of the signal is defined by the Carrier-to-Noise Ratio C/No, which is the ratio if the power level of the signal in 1 Hz bandwidth. The geometrical form of the city canyon defines the masking level of surrounding buildings. This affects directly signals transmitted from a low elevation angle. Thus, C/No and elevation angles values, as recorded by the receiver, are used to model the pseudorange observations noise variance.

Further information about the geometrical form of the canyon for a defined vehicle path allow us to determine, epoch by epoch, if the signals are received within multipath or not. This information provided from the Caploc Project [START_REF] Marais | Accurate localization based on gnss and propagation knwoledge for safe applications in guided transport[END_REF] will be used to introduce the our weighting model. Before presenting these models, let us remember some GNSS signal basis about user position computation.

The pseudorange observations equation can be written :

∆ρ = H∆X + (2)
H is the design matrix of the unit-vectors pointing from the linearization point to the location of the i-th satellite, and ∆X is the vector offset of the user's true position and time bias from the values at linearization point [START_REF] Kaplan | Undersatnding GPS : Principles and Applications[END_REF]. These observations are uncorrelated, and the errors are assumed to be normally distributed according to ∼ N (0, Σ). The inverse of the covariance matrix Σ will be used as the weighting matrix W , with the assumption that H T Σ -1 H is non-singular. The weighted least squares solution is :

∆ X = (H T Σ -1 H) -1 × H T Σ -1 ∆ρ, (3)
The matrix Σ is a diagonal matrix, where the diagonal elements are constituted of the rms of the σ 2 , for a specified model. Whatever the used model, the geometric and position DOP can be calculated using the expression (H T Σ -1 H) -1 .

We can find in literature some weighting models like the sigma- [START_REF] Hartinger | Variances of gps phase observations : The sigma-e model[END_REF], sigma-∆ [START_REF] Brunner | Gps signal diffraction modemodel : the stochastic sigma-δ model[END_REF] and exponential model [START_REF] Li | The improvement of positioning accuracy with weighted least square based on snr[END_REF]. These models link the C/No to the variance of the pseudorange measurements errors by means of some specified parameters.

A. Sigma-and elevation model

Concretly, the sigma-model uses the CNo values of the GPS signals to estimate weights for least square adjustment [START_REF] Hartinger | Variances of gps phase observations : The sigma-e model[END_REF]. Langley [START_REF] Langley | Gps receiver system noise[END_REF] has derived a formula that expresses the phase variance σ 2 as a function of the recorded C/No values. This formula was used for geodetic receiver. Wieser [START_REF] Wieser | An extended weight model for gps phase observations[END_REF] has proposed a completed formula that goes with all receiver types :

σ 2 se = v i + c i • 10 -0.1×CN o measured (4)
where v i (m 2 ) and c i (m 2 Hz) are model parameters and i is the frequency index (L 1 or L 2 ).

As in [START_REF] Hartinger | Variances of gps phase observations : The sigma-e model[END_REF], one should notice that the function 1/ sin 2 (θ i ) (θ i is the elevation angle of the satellite) can be a good estimate for the error variance and weighting function. The weights increase with the elevation angle.

These two models present some lacks in a strong multipath envionment. Actually, in the sigma-model, the variance σ 2 se does not change with the signal being LOS or NLOS, it changes only with C/No changing. On the other hand, the elevation model is not always beneficial for low elevation angles (multipath). For instance we can find a very low satellite with a relatively high C/No (fig. 1). That is why we have developed a complete model that consider both C/No and the elevation angle of a received signal at the same time. In this model, the variance σ 2 sr is changing with the elevation angle of the received signal and its carrier-to-noise density power. Since variance increases with multipath, this ratio is then multiplied by a coefficient k, k is determined whether the signal is LOS or NLOS. The state of reception of the received signal can be determined as in the Caploc Project, presented in the next paragraph.

B. C/No -Elevation model : Image analysis contribution

The Caploc project proposes a solution based on combining the image analysis and knowledge about the signal propagation for localization applications. The aim of this project is to classify, in a deterministic way, the received signals depending on the state of reception. The system developped in this project uses a camera with a fisheye lens. During the acquisition campaign, the camera records images of the surrouding environment. The pixels of the recorded images are classified into two zones : sky and non-sky (fig. 2) and (fig. 3). This classification permits to detect the mask caused by the buildings and other elements (fig. 2), and therefore to determine the position of the satellites in this sky map (fig. 3).The sky zone denotes the LOS received signals, while in the non-sky zone, signals are supposed to be received after one or many reflections.

The variance of the C/No -Elevation model is :

σ 2 sr = k × 10 (-0.1×CN o measured ) sin 2 (θ i ) (5)
When the received signal is LOS, k is supposed equal to 1. Whereas, when it is NLOS, k changes. In this paper we have computed the weights w sr = 1/σ 2 sr for k = 1, 2 and k = +∞.

IV. MEASUREMENTS CAMPAIGN AND FIRST RESULTS

To validate the proposed algorithms, we have used measurements realized on June 2010 in the city of Belfort, France. Data acquisition was performed with a 1 Hz frequency Septentrio receiver for the NMEA data and 27 Hz for the camera. The path we are using here has a duration of about 71 GPS positions for Septentrio and 171 points for the RTK system.

For illustration, fig. 4 shows the RTK trajectory, along with GPS positions computed with our C/No -elevation model (CE model), elevation model and ordinary least squares method. This figure shows a good improvement of the vehicle position computation when the CE model is used.

The figure 5 shows the vehicle position errors with respect to the RTK trajectory. Positions computed with the CE model (k = 2) present a very low error level. In table I, we have drawn the standard deviation (σ) and the root mean square errors values for all methods. We can see that there is a deviation improvement of 76.89% and RMS improvement of 72%. When k = 1, a good position is obtained also (table II), but it still less important that k = 2.

We have also tried the solution about excluding the NLOS signals by using the CE method with k = +∞. This means that the variance σ 2 sr is infinite and the weights w sr are equal to zero. Thereby, NLOS signals are excluded from position computation.

When only methods excluding GPS, such as OLS or CE model (k = +∞) are used, the position accuracy is highly degraded. Actually, as we can see in fig. 7, the acquisition zone constitutes a typical urban canyon with high and large buildings, dense vegetation, cross streets, . . . The yellow spot in this same figure indicates the map zone where NLOS are highly present. These multipath result in the outliers observed in fig. 6 (observations [0 : 23]) and fig. 4 (East [-20m : 20m]).

Our CE model including NLOS signals presents a very good solution for multipath problem in an urban canyon. On the same figures above, position accuracy is clearly improved when the CE model is used, even in the outliers zone.

V. CONCLUSION

The aim of our work is to develop a weighting model able to solve for multipath problem in an urban canyon environment.

In this paper, we have presented the CE weighting model which uses data about both carrier-to-noise density power of the received signal and its elevation angle. An image classification algorithm permitted us to decide if the received signal is LOS or NLOS. The CE model is then applied with a scalar (k) that changes according to the signal type.

The first results are very promoting, since we have noticed an improvement of 76.89% on the standard deviation value between the CE weighting model and OLS method.

In order to validate this model, we believe that it should be applied in other urban environments with strong multipath profiles. We have already performed another measurement campaign in a very dense district of Lille. On the other hand, it would be interesting to compare the performances of kalman filter and CE model in the same environment conditions, and to to implement real-time processors to compute vehicle position.

Figure 1 .

 1 Figure 1. C/No values for PRNs 22 (elev. angle ≈ 17 deg.) and 27 (elev. angle ≈ 70 deg.)

Figure 2 . 15 ]Figure 3 .

 2153 Figure2. Fish-eye camera image : detection of objects and vegetation edges[START_REF] Attia | Counting of satellites with direct gnss signals using fisheye camera : A comparison of clustering algorithms[END_REF]

Figure 4 .

 4 Figure 4. Reference trajectory RTK, CE model, elevation model and OLS vehicle position.

Figure 5 .

 5 Figure 5. Position errors (all models) with respect to the RTK trajectory, k = 2

6th

  European Workshop on GNSS Signals and Signal Processing, Munich, Allemagne, décembre 2013

Figure 6 .

 6 Figure 6. Comparison of position errors for some given values of k.

Table I .

 I STANDARD DEVIATION AND RMS ERROR VALUES FOR THE THREE MODELS, WITH k = 2

		OLS	CNo / Elevation	Elevation only
	Std deviation (m)	10.82	2.5	8.24
	RMS(m)	15.074	4.11	11.86

Table II .

 II STANDARD DEVIATION AND RMS ERROR VALUES FOR THE THREE MODELS, WITH k = 1

			OLS	CNo / Elevation	Elevation only
	Std deviation (m)	10.82	2.76	8.24
		RMS (m)	15.074	4.4	11.86
		50
					OLS
		40			k=inf k=1
					k=2
	Error (m)	20 30
		10
		0 0	20	40	60	80
			Nb of observations

Table III .

 III STANDARD DEVIATION AND RMS ERROR VALUES FOR THE THREE MODELS, WITH k = +∞

		OLS(m)	CNo / Elevation	Elevation only
	Std deviation (m)	10.82	15.74	8.24
	RMS	15.074	24.4	11.86

6th European Workshop on GNSS Signals and Signal Processing, Munich, Allemagne, décembre 2013


Josip Krapac

Florent Perronnin

Teddy Furon

Hervé Jégou

Instance classification with prototype selection

Keywords: Computer vision, image classification, feature selection

We address the problem of instance classification: our goal is to annotate images with tags corresponding to objects classes which exhibit small intra-class variations such as logos, products or landmarks. We propose a novel algorithm for the selection of class-specific prototypes which are used in a voting-based classification scheme. We show significant improvements over two state-of-the-art methods, namely the Fisher vector and Hamming Embedding, on two challenging methods of logos and vehicles.

INTRODUCTION

This paper deals with the task of image classification: given a query image, the goal is to predict the presence or absence of an object within a pre-determined set. We focus on instance classification, i.e. we consider objects with small intra-class variations such as logos, consumer products or landmarks. The applications are numerous, e.g. measuring brand exposure (logos), ensuring shelf compliance in the retail industry (products) or tagging consumer photos (landmarks). This problem is at the crossroad of two wellstudied problems in multimedia retrieval: object recognition and instance-level image retrieval. As in the case of instancelevel retrieval, we assume that the intra-class variability is mostly limited to extraneous factors such as viewpoint or lighting. However, as in object recognition, we assume that a small number of images is annotated with object labels to learn the object models.

We show that this instance classification is still not solved by current approaches to object recognition and instancelevel search, and we propose a new method that outperforms the state-of-the-art. Our main contribution is a novel algorithm which automatically selects class-specific features which we refer to as prototypes (see Fig. 1). For each prototype we also learn a distance threshold, such that features This work was done in the context of the FIRE-ID ANR Project (ANR-12-CORD-016). Preprint version published on February 5 th 2014. below this threshold with high probability describe the same object as the prototype. In the query phase the prototypes are used in a voting-based mechanism to compute per-class scores. Our method is simple, efficient and flexible: we obtain very good performance without the use of geometric layout information, and we scale well with the addition of new training examples and object classes.

The paper is organized as follows. Section 2 reviews the state-of-the-art in object recognition and instance-level image retrieval. Section 3 describes the proposed approach for instance classification based on prototype selection. Section 4 finally shows that our method outperforms popular state-of-the-art approaches for object classification and instance retrieval on two datasets, namely the public FlickrL-ogos32 dataset [START_REF] Romberg | Scalable logo recognition in real-world images[END_REF] and a new dataset of vehicle images.

RELATED WORK

Since its introduction, the bag-of-words (BoW) image representation has been widely used for object recognition [START_REF] Csurka | Visual categorization with bags of keypoints[END_REF] and image retrieval [START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF]. The first step in the BoW pipeline is to represent an image with a set of image patches. The patches are selected either using interest point detectors [START_REF] Mikolajczyk | A comparison of affine region detectors[END_REF] or sampled densely to cover the whole image. Each patch is then described by a local descriptor that captures the appearance of a patch, e.g., a SIFT vector [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF]. The distance in the space of local descriptors reflects visual similarity between patches. The descriptor space is partitioned using a quantizer (e.g. k-means) learned from a subset of local descriptors. Local descriptors are coded using the learned visual dictionary: they are mapped to the visual word index, i.e. the quantization cell they belong to. In the BoW, patches are compared via their codes: they are deemed similar when they are assigned to the same visual word. Extensions such as the Fisher Vector (FV) [START_REF] Perronnin | Fisher kernels on visual vocabularies for image categorization[END_REF] use coarser vocabularies but encode more information per cell than just an index, leading to state-of-the-art results in classification [START_REF] Perronnin | Improving the Fisher kernel for large-scale image classification[END_REF][START_REF] Chatfield | The devil is in the details: an evaluation of recent feature encoding methods[END_REF] and retrieval [START_REF] Jégou | Hamming embedding and weak geometric consistency for large scale image search[END_REF][START_REF] Jégou | Aggregating local images descriptors into compact codes[END_REF].

Two main strategies have been adopted to deal efficiently with the fact that the image is represented as a collection of patches: aggregation and inverted lists. In aggregation the patch codes of the image are pooled into a vector representation, such as a histogram of the visual word indices assigned to image patches [START_REF] Csurka | Visual categorization with bags of keypoints[END_REF]. The image is thus embedded into a vector space and the similarity between images is computed by evaluating a kernel function, such as the cosine similarity. Such aggregated representations are often used for image classification to learn a parametric model of a class using, for instance, a support vector machine (SVM). Inverted lists [START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF][START_REF] Jégou | Hamming embedding and weak geometric consistency for large scale image search[END_REF] on the other hand do not collapse the descriptor codes, but instead use them for indexing. This allows more precise matching, which is required for applications such as instance-based image retrieval.

Boiman et al. [START_REF] Boiman | In defense of nearest-neighbor based image classification[END_REF] argue that the main drawbacks of the BoW methods for object recognition are the quantization and the image-to-image distances. They showed good classification performance without quantizing descriptors and using an image-to-class distance. Several extensions of this model have been proposed, targeting class inbalance [START_REF] Behmo | Towards optimal naive Bayes nearest neighbor[END_REF] and efficiency [START_REF] Mccann | Local naive Bayes nearest neighbor for image classification[END_REF]. Our work is related to these Nearest Neighbor (NN) classifiers. We also do not quantize descriptors. However, instead of using all training set descriptors, we identify and use only a subset that allows reliable class prediction. Different from NN classifiers which use the distance to the class descriptor as a vote, the votes for the class are based on estimated class posteriors in neighborhood of the prototypes. The main advantage of our method wrt. both NN classifiers and BoW methods is that the score for the image is influenced only by the patches that are close to prototypes, therefore achieving robustness to varying object backgrounds.

PROPOSED ALGORITHM

This section describes our method to select prototypes and class scoring based on votes given to prototypes.

Notations. Suppose the training set contains M images of C classes. The i-th image of the training set associated to class label yi is represented by its set of local features

Xi = {x 1 i , • • • x N i i },
where Ni denotes the number of the extracted patches. Given a class y, we form its positive set by taking all patches from the My associated training images: Xy = ∪y i =y Xi. The patches from the other training images form the negative set of class y. Note that this is weakly supervised because we do not require any bounding box around objects. Thus, the positive set usually contains also some features from the background.

Prototype selection. The prototypes for a given class y are selected from Xy. We require that their neighborhood contains a high proportion of descriptors coming from different positive images, while the descriptors of the negative set are far away. To quantify this property we propose a new measure which we call patchAP. We use distances between the prototype candidate and train images to rank the images and we define patchAP as average precision of this ranking (c.f. left part of the Fig. 2). This corresponds to an area under the PR curve that displays image precision against image recall.

Formally, for a given feature x i of the i-th image, we first compute the distance dj to all images j = i: dj = minx∈X j xx i 2. These M -1 images are sorted by increasing distances: j1, . . . , jM-1. We define the class indicator function I(k) = 1 if yj k = yi, and else 0, and the cumulative sum J(r) = r k=1 I(k). The patchAP is:

patchAP = 1 My i -1 M -1 k=1 1 k I(k)J(k). (1)
A patch is selected as a prototype of the class if its patchAP is larger than a predefined threshold tpAP. The distribution of patchAP values varies across classes, so different classes are represented by a different number of prototypes.

If the local neighborhood of a feature contains a large proportion of patches coming from different positive images the patchAP of the feature is high. If the patches come from a small number of positive images, patchAP is small, since we consider only one patch per image. This way, we enforce that prototypes are both class-specific and that they occur in many different positive images, i.e. that they generalize well across images. As shown in Fig. 1, the selected prototypes are mostly located on the objects. This, as a side-product of our approach, enables to discover objects' discriminative parts and their locations automatically.

Radius selection. For a given prototype, we determine a distance threshold that is a radius of a prototype-centered ball. We require that the precision, i.e. the proportion of the positive patches within the ball, is higher than a threshold. Instead of just one radius we have a pre-determined set of ball precisions which yield a set of radii: the balls corresponding to lower precisions are larger. Notice that each prototype ends with its own set of radii. The precisions range from t bp to 1, where t bp denotes the minimum required ball precision. This is a per-prototype set of radii: prototypes in different parts of the feature space have a different ball radius for a given precision depending on the local density of the class (c.f. Fig. 3). This is different from NN classifiers based on distances that do not change across feature space.

Class scoring. Given a set of class prototypes equipped with their own set of radii, we compute the class scores for a query image as follows. Each patch extracted from the query image casts a vote. We determine into which balls the patch falls by comparing the distances to the prototypes with their radii. We select only the smallest ball for each prototype. Out of these, the patch votes only for the ball with highest precision. If there are several such balls, the patch vote is divided between them equally (c.f. right part of the Fig. 2). The ball vote is determined as the sum of all given patch votes. Next, each ball votes for its prototype with a weight that equals its associated precision. Finally, the score for a class is detemined as the sum of the class prototypes' votes.

A scalable implementation. Since the number of patches in the training set is large (≈ 10 8 on FlickrLogos32), the patchAP of a given feature is computed only from the k nearest neighbor patches. The Product Quantization scheme (PQ) provides a fast approximate nearest neighbors search [START_REF] Jégou | Aggregating local images descriptors into compact codes[END_REF]. We used it to shortlist k closest points from the training set and re-rank them by computing the exact distances. The ball radii corresponding to the precision thresholds are computed in the same k-neighborhood.

PQ is also used in the test phase, to compute the class scores for the query image: the prototypes for all classes selected in the training phase compose the database. Then, for each patch of a query image, PQ finds the k nearest prototypes, and we compute the exact distances from these shortlisted prototypes, which we use to obtain class scores.

Notice that the scores for all classes are derived at a constant time cost of querying PQ and computing the shortlisted distances. This setup scales well with addition of new labeled data: adding classes or training images amounts to adding the newly computed prototypes into the database.

Parameter selection. The method has two parameters: the threshold on patchAP tpAP and the minimum ball precision t bp . The former determines the number of selected prototypes, while the t bp determines the number of balls per prototype. We perform a grid search and select the parameters tpAP and t bp that yield the best accuracy on the training data.

EXPERIMENTS

We first describe the datasets, the features and the experimental setup. We then provide a comparative evaluation of the proposed approach based on the mean average preci- sion (mAP), which is commonly defined as the mean of the per-class average precisions.

Datasets. The FlickrLogos32 dataset [START_REF] Romberg | Scalable logo recognition in real-world images[END_REF] contains 8,240 images of 32 logo classes. The dataset is divided into three sets. The first set contains 10 images per class of closeup logos with limited background. The second and third sets both contain 30 images of logos per class and 3,000 distractors (i.e., images that do not contain any logos) of various sizes displayed against various backgrounds. We use the first two sets to extract the prototypes and for parameter tuning, and the remaining set to test the method. So far, this dataset has been tested only for image retrieval, but we believe it is also very relevant for instance classification.

We also introduce the Vehicles29 dataset which we collected by querying 29 car models of 7 brands to a secondhand ads website. Each manufacturer is represented by 3 to 6 models. A class may contain multiple submodels corresponding to the years of production. In total, there are 10,622 images, divided into 5,266 training and 5,356 test images. On average, there are 150 training and testing images per car model. The dataset is very challenging as some cars are very similar and differ only in small details like front mask, door handles, lights or position of wiper.

Local features are SIFT descriptors [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF] extracted from points detected by the the rotation-invariant Harris-Hessian-Laplace interest point detector [START_REF] Mikolajczyk | A comparison of affine region detectors[END_REF]. Following prior work [START_REF] Jain | Hamming embedding similarity-based image classification[END_REF], the descriptors are 2-normalized to the unit ball and squarerooted as these normalization steps were shown to improve matching performance. Experimental setup. For each candidate prototype, the patchAP is computed from a k-neighborhood of size 20, 000. The radii for these prototypes are computed for a set of 20 precisions in range [0.05, 1] with a step size of 0.05. The scores for the query image are computed from 10, 000 nearest prototypes for each detected patch.

Justification of the proposed approach. Fig. 3 shows that the ball precision (the proportion of the class patches inside the ball) varies considerably for a given radius. Patch votes should reflect class membership whose degree of confidence we capture by the ball precision. This justifies our approach: determine offline the radii at which the required class precision is attained, so that, online, patches falling into such balls cast a vote directly linked to the degree of confidence. This is better than determining the patch vote based on its distance to the class prototype. Parameter analysis. Fig. 4 shows the influence of the parameters on the performance on the FlickrLogos32 dataset.

The behavior is similar on Vehicles29 dataset, but at the lower range of patchAP thresholds. Logos are, by design, discriminative and unique and therefore match well over many training images, resulting in prototypes with high patchAP. On the other hand, car classes can contain visually different vehicles, so patches may be matched across a smaller number of training images, which means that selected prototypes have lower patchAP values. Lower tpAP, corresponding to larger number of prototypes, and high t bp corresponding to small number of high precision balls per prototype, gives good performance on both datasets.

Qualitative analysis. Our method succeeds in selecting discriminative parts of the objects. Although the prototypes are extracted in a weakly-supervised manner, i.e., without any bounding boxes, the vast majority of them lies on the object, as can be seen from Fig. 1. Notice that the supervised setting (e.g., bounding boxes) would not help in the case of cars since only a subset of patches detected on the object is important to discriminate the classes.

Performance comparison. In the second set of experiments presented in Table 1, we compare the proposed method to baselines. The proposed method is most related to NBNN [START_REF] Boiman | In defense of nearest-neighbor based image classification[END_REF], as we also do not quantize features. However, we use aggregate class posteriors rather than distance to obtain class scores and only a selected subset of all training features contributes to the class score. This significantly influences the performance. We compare also to the Fisher Vector (FV) [START_REF] Perronnin | Improving the Fisher kernel for large-scale image classification[END_REF] which is the state-of-the-art for patch-based object recognition [START_REF] Chatfield | The devil is in the details: an evaluation of recent feature encoding methods[END_REF]. We experimented with two settings: a "standard" setting where, following [START_REF] Perronnin | Improving the Fisher kernel for large-scale image classification[END_REF], we used a 256-component mixture-of-Gaussians and a "costly" setting where we used 4,096 components (thus leading to 524,288-dim FVs). A linear one-vs-all support vector machine (SVM) is learned for each class. For logo classification, we also compare to Hamming Embedding (HE), the state-of-the-art for image retrieval. In this case, we use a k-NN classifier with k=40.

For each test image, we get HE scores for logo images in the train set using a Hamming threshold ht = 20. All compared methods use all query image features to obtain class Comparison to the state-of-the-art. Using precision rather than distance, and selecting prototypes improves results significantly wrt. NBNN. k-NN classifier using Hamming Embedding (HE) scores performs comparably to FVs with 256 Gaussian components. Increasing the number of Gaussians improves performance, but with diminishing returns.

scores. The proposed method computes the similarities between query features and class prototypes. Therefore only the query features in the neighborhood of the class' prototypes influence the class score.

CONCLUSION

This paper introduced a method for visual instance classification based on the automatic selection of class representatives -class prototypes. The method performs favorably to state-of-the-art approaches in object classification and image retrieval, as demonstrated experimentally on two challenging datasets of logos and vehicles. Our method selects the prototypes independently, so they are redundant. In addition, all prototypes are weighted equally. Learning their relative importance may improve the classification performance. To this end, the combination with sparse linear models, e.g. [START_REF] Wang | Learning class-to-image distance via large margin and L1-norm regularization[END_REF], is a promising research direction.

Figure 1 :

 1 Figure 1: Prototypes with high patchAP. Left: images from the FlickrLogos32 dataset. Right: images from the Vehicles29 dataset. The selected prototypes reveal discriminative parts of the objects.

Figure 2 :

 2 Figure 2: Illustration of the method. Left: Prototype selection. The patches from the positive set are red, the ones from the negative set blue. The numbers denote the images they are extracted from, the circles and the squares the distances to the closest patches from different images. The patchAP corresponds to average precision of the ranking of the squares. The patchAP is equal to 1 when all red squares are ranked before the blue ones. Right: Ball assignment. Two patches (a,b) from a query image, scoring two prototypes (red, blue). The precision of the ball is denoted up left. Although both patches fall into two balls, patch a is assigned only to the ball with higher precision (dark blue), while the contribution of the patch b is divided between two balls having equal precision. Best viewed in color.

Figure 3 :

 3 Figure 3: Histogram of ball sizes for 3 precisions. Balls associated to the same precision vary in size considerably. Balls with the same radius contain different proportions of patches of the same class.

  Figure4: Influence of the patchAP threshold t pAP and the ball precision threshold t bp on the accuracy on Flick-rLogos32. The behavior is similar for Vehicles29. Low t pAP and high t bp , which correspond to more prototypes and fewer high precision balls per prototype, yield better performance.

		0.9
	mAP	0.85
		0.8		t pAP =0.05
					t pAP =0.1
		0.75			t pAP =0.2 t pAP =0.3
		0.2	0.4	0.6	0.8	1
			ball precision threshold (t bp )

Table 1 :

 1

	Method	classification mAP FlickrLogos32 Vehicles29
	NBNN	5.25	5.36
	HE + kNN (k=40)	76.9	-
	Fisher Vector (256)	80.5	44.6
	Fisher Vector (4,096)	86.6	49.7
	Prototype voting	91.4	55.7

Acknowledgments. This work was done in the context of the FIRE-ID ANR Project (ANR-12-CORD-016).


Vanessa Delfosse

Marina Grimaldi

Albane Le Maire

William Bourguet
email: bourguet@cbs.cnrs.fr

Patrick Balaguer
email: patrick.balaguer@montpellier.unicancer.fr

Nuclear receptor profiling of bisphenol-a and its halogenated analogues

Keywords: 5-10): bisphenol-A, halogenated bisphenol-A, nuclear hormone receptor, endocrine disruptor I

Introduction

Human nuclear hormone receptors (NHRs) are a family of 48 transcription factors, many of which have been shown to be activated by ligands. NHRs regulate cognate gene networks involved in key physiological functions such as cell growth and differentiation, development, homeostasis, or metabolism [START_REF] Germain | Overview of nomenclature of nuclear receptors[END_REF][START_REF] Gronemeyer | Principles for modulation of the nuclear receptor superfamily[END_REF]. As a consequence, inappropriate exposure to environmental pollutants often leads to proliferative, reproductive and metabolic diseases, including hormonal cancers, infertility, obesity or diabetes. NHRs are modular proteins composed of several domains, most notably an N-terminal domain which harbors a ligand-independent activation function (AF-1), a central DNA binding domain (DBD) and a C-terminal ligand binding domain (LBD) hosting a ligand-dependent transcriptional activation function (AF-2) [START_REF] Gronemeyer | Principles for modulation of the nuclear receptor superfamily[END_REF]. In the absence of the cognate ligand, some NHRs are located in the nucleus, bind to the DNA response elements of their target genes and recruit corepressors, while others are located in the cytoplasm in an inactive complex with chaperones. Ligand binding induces major structural alterations of the receptor LBDs leading to (1) destabilization of corepressor or chaperone interfaces, (2) exposure of nuclear localization signals to allow nuclear translocation and DNA binding of cytoplasmic receptors and (3) recruitment of coactivators triggering gene transcription through chromatin remodeling and activation of the general transcription machinery. The crystal structures of many NHR LBDs have been determined, revealing a conserved core of 12 α-helices (H1-H12) and a short two-stranded antiparallel β-sheet (S1 and S2) arranged into a three-layered sandwich fold. This arrangement generates a mostly hydrophobic cavity in the lower half of the domain which can accommodate the cognate ligand. In all hormone-bound LBD structures, the ligand binding pocket (LBP) is sealed by helix H12. This conformation is specifically induced by the binding of hormones or synthetic agonists and is referred to as the ""active conformation"" because it allows the dissociation of corepressors and favors the recruitment of transcriptional coactivators [START_REF] Bourguet | Nuclear receptor ligand-binding domains: threedimensional structures, molecular interactions and pharmacological implications[END_REF][START_REF] Pike | Lessons learnt from structural studies of the oestrogen receptor[END_REF][START_REF] Renaud | Structural studies on nuclear receptors[END_REF]. It is noteworthy that this conformational state can also be achieved by some constitutively active orphan receptors for which no natural ligand has been identified. In this active-form, helices H3, H4 and H12 define a hydrophobic binding groove for short LxxLL helical motifs (L stands for leucine and x for any amino acid) found within coactivators. In contrast to agonist binding, interaction with antagonists prevents the correct positioning of helix H12, thus avoiding association with the LxxLL motifs of coactivators [START_REF] Bourguet | Nuclear receptor ligand-binding domains: threedimensional structures, molecular interactions and pharmacological implications[END_REF][START_REF] Pike | Lessons learnt from structural studies of the oestrogen receptor[END_REF][START_REF] Renaud | Structural studies on nuclear receptors[END_REF]. The LBD also contributes to the modulation of the N-terminal AF-1 through interdomain crosstalk so that both AF-1 and AF-2 domains can recruit a range of coregulatory proteins and act individually or in a synergistic manner [START_REF] Benecke | Synergy between estrogen receptor alpha activation functions AF1 and AF2 mediated by transcription intermediary factor TIF2[END_REF][START_REF] Bommer | TIF2 Mediates the Synergy between RARalpha 1 Activation Functions AF-1 and AF-2[END_REF][START_REF] Wilson | Analysis of interdomain interactions of the androgen receptor[END_REF]. The precise structural basis of this interdomain communication is unknown, as no 3D structure of an entire NR has been obtained.

Bisphenol-A (BPA) is one of the highest volume chemicals produced worldwide, with over 6 billion pounds produced each year. BPA enters into the composition of polycarbonate plastic, epoxy resins used in metallic food cans, dentistry sealants and thermal paper [START_REF] Vandenberg | Bisphenol-A and the great divide: a review of controversies in the field of endocrine disruption[END_REF]. Halogenated derivatives of BPA, which feature bromine or chlorine substituents on the phenolic rings, are used as flame retardants. Tetrabromobisphenol-A (TBBPA) is mainly used as a flame retardant to protect computer motherboards and other electronic equipment. Its production is currently estimated around 200,000 tons/year, and its presence has been reported in the environment (de Wit) and in wildlife [START_REF] Darnerud | Toxic effects of brominated flame retardants in man and in wildlife[END_REF]. Tetrachlorobisphenol-A (TCBPA) has also been reported to be used as a flame retardant, but in much lower quantities than TBBPA (<10,000 tons/year) [START_REF] Chu | Simultaneous determination of tetrabromobisphenol A, tetrachlorobisphenol A, bisphenol A and other halogenated analogues in sediment and sludge by high performance liquid chromatography-electrospray tandem mass spectrometry[END_REF]. The presence of TCBPA, as well as that of lower chlorinated analogues (monoCBPA, diCBPA and triCBPA) in environmental samples has been unequivocally demonstrated [START_REF] Fukazawa | Identification and quantification of chlorinated bisphenol A in wastewater from wastepaper recycling plants[END_REF][START_REF] Gallart-Ayala | Field-amplified sample injectionmicellar electrokinetic capillary chromatography for the analysis of bisphenol A, bisphenol F, and their diglycidyl ethers and derivatives in canned soft drinks[END_REF][START_REF] Liu | Formation of chlorinated intermediate from bisphenol A in surface saline water under simulated solar light irradiation[END_REF]. Contrary to TBBPA, and given the low levels of production of TCBPA, the origin of most chlorinated-BPA in the environment is more likely the chlorination of BPA than the dechlorination of TCBPA.

BPA or its halogenated derivatives have been shown to target several NHRs including the estrogen receptors (ERα, β), the androgen receptor (AR), the estrogen related receptor γ (ERRγ), the thyroid hormone receptors (TRα, β), the pregnane X receptor (PXR) and the peroxisome proliferator activated receptors (PPARα, γ, δ). The crystal structures of ERα and ERRγ in complex with BPA and of PPARγ bound to TBBPA or TCBPA have been reported recently. Here, we review recent studies showing the ways in which BPA and halogenated BPAs bind to and activate NHRs.

II. Estrogens receptors

Estrogen receptors (ERα and ERβ) are receptors for the sex hormone, 17β-estradiol (E 2 ), which play important roles in the growth and maintenance of a diverse range of tissues such as the mammary gland, uterus, bones or the cardiovascular system. Both ERs are widely distributed throughout the body, displaying distinct but overlapping expression patterns in a variety of tissues [START_REF] Couse | Estrogen receptor null mice: what have we learned and where will they lead us?[END_REF].

ERα is expressed primarily in the uterus, liver, kidney, and heart, whereas ERβ is expressed primarily in the ovary, prostate, lung, gastrointestinal tract, bladder, and hematopoietic and central nervous systems [START_REF] Kuiper | Comparison of the ligand binding specificity and transcript tissue distribution of estrogen receptors alpha and beta[END_REF]. However, ERα and ERβ are coexpressed in a number of tissues including the mammary gland, thyroid, adrenal, bones and some regions of the brain. Although ERα and ERβ share similar mechanisms of action, several differences in the transcriptional abilities of each receptor as well as distinct phenotypes between gene-null animals have been identified, suggesting that these receptors may regulate distinct cellular pathways [START_REF] Couse | Estrogen receptor null mice: what have we learned and where will they lead us?[END_REF][START_REF] Curtis | Physiological coupling of growth factor and steroid receptor signaling pathways: estrogen receptor knockout mice lack estrogen-like response to epidermal growth factor[END_REF].

ERs activity of bisphenols

BPA is considered as a weak environmental estrogen because of its relatively low affinity for the nuclear ERs compared with estradiol (10,000 to 100,000-fold lower affinity) [START_REF] Delfosse | Structural and mechanistic insights into bisphenols action provide guidelines for risk assessment and discovery of bisphenol A substitutes[END_REF][START_REF] Kitamura | Anti-thyroid hormonal activity of tetrabromobisphenol A, a flame retardant, and related compounds: Affinity to the mammalian thyroid hormone receptor, and effect on tadpole metamorphosis[END_REF][START_REF] Paris | Phenylphenols, biphenols, bisphenol-A and 4-tert-octylphenol exhibit alpha and beta estrogen activities and antiandrogen activity in reporter cell lines[END_REF]. Several studies indicated that BPA is a partial agonist [START_REF] Gould | Bisphenol A interacts with the estrogen receptor alpha in a distinct manner from estradiol[END_REF][START_REF] Routledge | Differential effects of xenoestrogens on coactivator recruitment by estrogen receptor (ER) alpha and ERbeta[END_REF]. In a recent work, we have confirmed that BPA is a selective estrogen receptor modulator (SERM) that functions in a cell-selective manner [START_REF] Delfosse | Structural and mechanistic insights into bisphenols action provide guidelines for risk assessment and discovery of bisphenol A substitutes[END_REF]. Our data reveal that BPA activity relies mostly on the AF-1 and depends on the cellular context. In this study, we compared BPA with different bisphenols for their affinity and activity using HeLa ER and ER reporter cell lines. For ERα and ER affinity, the ranking order was BPC > BPAF > BPB > BPA > BPE > BPF > BPS. For activity, the ranking order is almost the same for ER and ER. It is BPF = BPE = BPS > BPA > BPC = BPAF = BPB, BPC being less active on ER than ER. The potency likely originates from the differential synergy between AF-1 and AF-2 and this synergism is probably more important in the HeLa cellular context for ER than for ER.

In two other studies (Riu, 2011a;[START_REF] Riu | Characterization of novel ligands of ERalpha, Erbeta, and PPARgamma: the case of halogenated bisphenol A and their conjugated metabolites[END_REF], we have characterized the estrogenic activity of TBBPA and TCBPA together with lower halogenated BPA. For brominated analogues, the ranking order of estrogenic potency on ER and ER was monoBBPA > diBBPA > triBBPA while TBBPA showed no estrogenic activity at all. Chlorinated BPA analogues are at least as potent agonists as BPA for ERα as already published by others groups [START_REF] Mutou | Change of Estrogenic Activity and Release of Chloride Ion in Chlorinated Bisphenol A after Exposure to Ultraviolet B[END_REF]Takemura, 2005). Contrary to brominated BPA, the halogenation degree of chlorinated bisphenols did not decrease their ER potency. Likely due to the lower ligand binding pocket size of ER compared to ERα, chlorinated analogues with the lowest molecular weight (mono-and diCBPA) exhibited the highest agonistic activity on ER.

Structures of BP-bound ERs

Structures of the complexes between ERα and BPA, BPAF, and BPC were recently reported [START_REF] Delfosse | Structural and mechanistic insights into bisphenols action provide guidelines for risk assessment and discovery of bisphenol A substitutes[END_REF] and their comparison with that of the E 2 -and the OHT-bound ERα allowed the description of the binding mode of these BPs and the explanation of their different activities and binding affinities. The structures with BPA, BPAF and TCBPA display the canonical active conformation with H12 capping the LBP and the LxxLL-containing coactivator peptide bound to the AF-2 surface (Figure 2A). The structure with BPC displays an antagonist conformation similar to that observed in the OHT-bound structure (PDB code 3ERT) with H12 occupying the coactivator binding groove (Figure 2A). The structures also reveal two divergent binding mechanisms of BPs.

BPA adopts a binding mode reminiscent of that used by E 2 with the two phenol groups hydrogen bonded to three polar residues located at the two ends of the pocket, namely H524 (H11) on one side and E353 (H3) and R394 (H5) on the other side (Figure 2B and 2C). The remaining contacts involve van der Waals interactions. In contrast, BPC is positioned in the pocket so as to draw the phenol ring B into an alternate position as compared with that of the corresponding ring in BPA and TCBPA. A rotation by 180° around the main axis of phenol ring A orients ring B towards H12 (Figure 2D).

Finally, in the BPAF complex each subunit of the ERα homodimer contains one BPAF molecule with the "BPA-like" or "BPC-like" positioning. The different activities of BPs could be attributed to the destabilization of the AF-2 surface as many of the previously recognized ligand -H11 stabilizing interactions observed in the E 2 -bound structure are altered in the bisphenol-containing complexes [START_REF] Bruning | Coupling of receptor conformation and ligand orientation determine graded activity[END_REF][START_REF] Delfosse | Structural and mechanistic insights into bisphenols action provide guidelines for risk assessment and discovery of bisphenol A substitutes[END_REF][START_REF] Nettles | NFkappaB selectivity of estrogen receptor ligands revealed by comparative crystallographic analyses[END_REF]. One of the key differences resides in the differential interaction of the various ligands with L525. In the E 2 -bound structure, E 2 imposes a conformation of this leucine that strengthens a network of van der Waals interactions involving T347, L525 and L536 (Figure 2A). This cluster of interactions is of utmost importance because it holds together helices H3, H11 and the loop preceding H12, thereby stabilizing the AF-2 surface. In the structure with BPA (Figure 2B), the stabilizing interaction between the bisphenol and L525 is absent. This renders L525 more dynamic so that its side chain adopts different conformations in the two subunits of the homodimer. The situation is even worse in the structure with BPC where the side chain of T347 rotates by 180° to form a hydrogen bond with the hydroxyl moiety from the phenol ring B of BPC (Figure 2D). This loss of stabilizing contacts provoked by bisphenols renders the lower part of the ERα LBP more dynamic. Indeed, this portion of LBDs has been previously shown to have some of the characteristics of a molten globule and a large part of the agonistic properties of a ligand relies in its capacity to stabilize this region encompassing the H3/H11 docking surface for H12 in the active conformation [START_REF] Gee | Probing conformational changes in the estrogen receptor: evidence for a partially unfolded intermediate facilitating ligand binding and release[END_REF][START_REF] Nagy | Mechanism of the nuclear receptor molecular switch[END_REF]. The complete disruption of the hydrophobic cluster by BPC probably accounts for the marked antagonistic character of this bisphenol. Modelling studies indicated similar binding modes in ERβ [START_REF] Delfosse | Structural and mechanistic insights into bisphenols action provide guidelines for risk assessment and discovery of bisphenol A substitutes[END_REF].

III. Estrogen related receptor 

ERR is a member of the ERR subfamily of orphan receptors, which are closely related to ERs [START_REF] Giguere | To ERR in the estrogen pathway[END_REF] The ERR family includes three members, ERRα, ERRβ and ERR. The three receptors are very similar, with 90% sequence identity in the DBD and more than 60% in the LBD.

ERR is expressed in a tissue-restricted manner, for example very strongly in the mammalian brain during development, and then in the brain, lung and many others tissues during adulthood. In terms of structure, ERR is very close to ERs. Sequence alignment reveals a 60% identity in the DBD regions and a moderate similarity (<35%) of the LBDs, consistent with the incapacity of ERR to bind E 2 [START_REF] Horard | Estrogen receptor-related receptors: orphan receptors desperately seeking a ligand[END_REF]. Nevertheless, it has been demonstrated that ERR can interfere with estrogen signaling [START_REF] Giguere | To ERR in the estrogen pathway[END_REF]. Indeed, ERs and ERR recognize the same DNA binding elements, share common target genes and are coexpressed in many tissues [START_REF] Lu | Transcriptional regulation of the estrogeninducible pS2 breast cancer marker gene by the ERR family of orphan nuclear receptors[END_REF]Vanacker, 1999).

Exogenous overexpression of ERR in prostate cancer cell line results in inhibition of proliferation [START_REF] Yu | Figure PPAR: Crystal structures of PPARγ LBD in complex with TBBPA and TBBPA-sulfate. (A) Overall structure of the TBBPA-bound PPARγ LBD. The polypeptide backbone is illustrated as a grey ribbon and TBBPA is shown in stick representation. (B) Superimposition of the co-crystal structure of TBBPA-bound PPARγ LBD (in black) on the structure with rosiglitazone (grey, PDB code 2PRG). (C) Superimposition of the co-crystal structure of PPARγ LBD bound to TBBPA-sulfate (black) on the structure with TBBPA (grey). Roziglitazone, TBBPA and TBBPA-sulfate are shown in stick representation[END_REF]. Furthermore, treatment with an ERRβ/ agonist has been shown to promote this antiproliferative effect, consistent with ERR being a favorable prognosis factor [START_REF] Ariazi | Estrogen-related receptors as emerging targets in cancer and metabolic disorders[END_REF].

Additionally, several lines of evidence suggest that ERRs play a central role in regulating energy metabolism. Genetic studies in mice reveal that their presence is essential for the generation of energy and related tissue-specific functions, and functional genomics/proteomics studies have associated ERR with the control of vast metabolic gene networks, in particular those involved in mitochondrial biogenesis and function [START_REF] Giguere | Transcriptional control of energy homeostasis by the estrogen-related receptors[END_REF]. The rise in the incidence of metabolic syndromes correlates with the rise in the use and distribution of industrial chemicals that may play a role in generation of obesity [START_REF] Baillie-Hamilton | Chemical toxins: a hypothesis to explain the global obesity epidemic[END_REF], suggesting that EDCs and ERR may be linked to this epidemic crisis. To date, the ERR have not been shown to interact with any physiologically relevant small molecules, suggesting that these receptors manifest constitutive activity [START_REF] Greschik | Structural and functional evidence for ligand-independent transcriptional activation by the estrogen-related receptor 3[END_REF][START_REF] Li | In vitro profiling of endocrine disrupting effects of phenols[END_REF], and, indeed, crystallographic analyses of ERR indicated that these receptors adopt the transcriptionally active conformation in the absence of any ligand [START_REF] Greschik | Structural and functional evidence for ligand-independent transcriptional activation by the estrogen-related receptor 3[END_REF].

ERR activity of bisphenols

Compounds screening for activity on ERR have identified diethylstilbestrol and 4hydroxytamoxifen as inverse agonists and BPA as agonist for ERR [START_REF] Coward | 4-Hydroxytamoxifen binds to and deactivates the estrogen-related receptor gamma[END_REF]Okada, 2008;Tremblay, 2001). Among bisphenols, BPA, BPE and BPB have been found to have the highest affinity for ERR [START_REF] Li | In vitro profiling of endocrine disrupting effects of phenols[END_REF]Okada, 2008). Interestingly, these two studies have enabled to discriminate between ER and ERR selective agonists. BPA could be considered as a pan agonist for ER. BPAF and BPC could be considered as ER selective agonists and BPE and BPF as ERR selective agonists. It is not surprising that these ligands can be used as tools to determine the respective roles of ER and ERR in cells or organs co-expressing these two receptors.

Structural basis of BPs interaction with ERR

Although a natural ligand remains to be found for ERR, several synthetic ligands have been identified for this receptor [START_REF] Li | In vitro profiling of endocrine disrupting effects of phenols[END_REF]Okada, 2008). All display a conserved phenol ring such as BPs.

The structure of ERR in complex with BPA and BPZ have been solved, revealing an overall protein conformation indistinguishable from that of the unliganded receptor [START_REF] Abad | Structural determination of estrogen-related receptor gamma in the presence of phenol derivative compounds[END_REF][START_REF] Matsushima | Structural evidence for endocrine disruptor bisphenol A binding to human nuclear receptor ERR gamma[END_REF]Matsushima, 2008) (Figure 3A). A close look at the LBP shows that, as previously anticipated, one of the two phenol-hydroxyl groups of BPA and BPZ forms hydrogen bonds with residues E275 (H3) and R316 (H5) while the second is hydrogen bonded to N346 in H7 (Figure 7).

A hydrogen bond between Y326 and N346 holds N346 in position to interact with the second phenol group of BPs. Interestingly, this asparagine residue is not conserved in ERRα and β, thus accounting for the specific ERR-BPs interaction. Moreover, comparison of ERR and ERRα LBPs reveals a much smaller cavity for the latter [START_REF] Kallen | Evidence for ligand-independent transcriptional activation of the human estrogen-related receptor alpha (ERRalpha): crystal structure of ERRalpha ligand binding domain in complex with peroxisome proliferator-activated receptor coactivator-1alpha[END_REF]. The replacement of two alanine residues (A272 and A431) in ERR by a phenylalanine (F328) and a valine (V491) in ERRα accounts for this size reduction and further explains why BPA does not bind to the latter. BPs binding provokes only minimal LBP rearrangements (Figure 3B). E275, which appears disordered in the unliganded structure, adopts a unique conformation to make a hydrogen bond with one OH group of BPs, and the side chain of L345 moves away from the pocket upon BPs binding to open up the cavity and make room for the second phenol group of BPs. In summary, ERR possesses a LBP to which BPs can bind with high affinity and specificity while preserving the constitutively active conformation of the receptor. The limited impact of BPA binding on receptor structure is consistent with the fact that this ligand does not enhance or disrupt coactivator binding and thus appears as functionally silent ligand [START_REF] Abad | Structural determination of estrogen-related receptor gamma in the presence of phenol derivative compounds[END_REF][START_REF] Matsushima | Structural evidence for endocrine disruptor bisphenol A binding to human nuclear receptor ERR gamma[END_REF]. Thus, the classical mechanism of NHR activation involving the re-localization and stabilization of helix H12 in the active conformation does not explain how ERR could mediate the estrogenic effects of BPs. Rather, thermal stability studies revealed that BPA binding leads to global thermodynamic stabilization of ERR LBD, a phenomenon which could increase steady state levels of the receptor and impact both its cellular half-life and biological activity [START_REF] Abad | Structural determination of estrogen-related receptor gamma in the presence of phenol derivative compounds[END_REF][START_REF] Matsushima | Structural evidence for endocrine disruptor bisphenol A binding to human nuclear receptor ERR gamma[END_REF][START_REF] Wang | X-ray crystal structures of the estrogenrelated receptor-gamma ligand binding domain in three functional states reveal the molecular basis of small molecule regulation[END_REF]. A recent modeling study indicated that in ERRγ all bisphenols adopt the agonist BPA-like position observed in ERα due to the hydrogen bond with N346 from helix H7. This in silico result correlates both with functional data showing that bisphenols are ERRγ activators [START_REF] Delfosse | Structural and mechanistic insights into bisphenols action provide guidelines for risk assessment and discovery of bisphenol A substitutes[END_REF] and the crystal structure of ERRγ in complex with BPA [START_REF] Abad | Structural determination of estrogen-related receptor gamma in the presence of phenol derivative compounds[END_REF][START_REF] Matsushima | Structural evidence for endocrine disruptor bisphenol A binding to human nuclear receptor ERR gamma[END_REF].

IV. Androgen receptor

AR plays crucial role in the regulation of target gene expression in physiological processes like development and differentiation of the male embryo and spermatogenesis initiation and maintenance, as well as neuro-endocrine system functioning [START_REF] Matsumoto | The Androgen Receptor in Health and Disease[END_REF]. The central role of AR has been verified by AR-deficient mice (AR-KO) and by hereditary disorders of androgen insensitivity syndrome in human males. AR-KO mice display an array of phenotypes involving several organs and cell types. Reproductive tract and gonadal development as well as sexual behavior are severely impacted. In humans, AR mutations cause abnormalities from mild virilization defects to complete male to female sex reversal. These mutations lead to either complete (CAIS) or partial (PAIS) androgen insensitivity syndromes [START_REF] Mcphaul | Molecular defects of the androgen receptor[END_REF][START_REF] Quigley | Androgen receptor defects: historical, clinical, and molecular perspectives[END_REF]. In the absence of ligands, AR is localized essentially in the cytoplasm. Binding to androgens enable HSPs dissociation and AR translocation to the nucleus. The AR LBD strongly contributes to the modulation of the Nterminal AF-1 through ligand-induced interdomain association. Furthermore, in AR, it appears that AF-1 predominates over AF-2 [START_REF] He | FXXLF and WXXLF Sequences Mediate the NH2-terminal Interaction with the Ligand Binding Domain of the Androgen Receptor[END_REF].

Androgens are thus male sex hormones that are critical for the development and maintenance of the male reproductive system. The plasma androgen/estrogen ratio during fetal life creates a maleversus-female hormonal milieu [START_REF] Mclachlan | Estrogens and development[END_REF]. This delicate balance could be disrupted by environmental antiandrogens or estrogens and lead to hermaphroditism.

Finally, prostate development and prostate cancer are also critically dependant on androgens [START_REF] Mccarthy | Prostate cancer: Studying the classics[END_REF]. Current therapies of prostate cancers are primarily based on androgen antagonists that interact with AR and completely or partially block the hormone-responsive pathways.

AR activity of bisphenols

BPA is considered a weak environmental anti androgen because of its relatively low affinity for AR [START_REF] Li | In vitro profiling of endocrine disrupting effects of phenols[END_REF][START_REF] Paris | Phenylphenols, biphenols, bisphenol-A and 4-tert-octylphenol exhibit alpha and beta estrogen activities and antiandrogen activity in reporter cell lines[END_REF][START_REF] Stroheker | Steroid activities comparison of natural and food wrap compounds in human breast cancer cell lines[END_REF]. In a recent work, we have confirmed these results [START_REF] Delfosse | Structural and mechanistic insights into bisphenols action provide guidelines for risk assessment and discovery of bisphenol A substitutes[END_REF]. In this study, we compared BPA with different bisphenols for their anti-androgenic activity using an AR reporter cell line. The ranking order was BPC >> BPAF > BPA = BPB = BPE > BPF > BPS. It is noteworthy that BPC has the same potency than the vinclozolin metabolite M2 which is the most potent xenoantiandrogen [START_REF] Kelce | Vinclozolin and p,p'-DDE alter androgen-dependent gene expression: in vivo confirmation of an androgen receptormediated mechanism[END_REF][START_REF] Paris | Phenylphenols, biphenols, bisphenol-A and 4-tert-octylphenol exhibit alpha and beta estrogen activities and antiandrogen activity in reporter cell lines[END_REF].

As it was observed for estrogenic activity, TCBPA was able to inhibit AR activity while TBBPA was not [START_REF] Li | In vitro profiling of endocrine disrupting effects of phenols[END_REF] (P Balaguer , unpublished data). Interestingly, lower halogenated analogues were also AR inhibitors, mono-and di bromo and chloro-BPA being the most potent (P Balaguer, unpublished data). Interestingly, in a recent modeling study, all bisphenols appeared to bind to AR exclusively in the antagonist BPC-like orientation, in agreement with the observation that these compounds act as AR antagonists. This orientation appears to be stabilized by formation of a hydrogen bond between one hydroxyl group of the ligand and N705, a polar residue specific of AR [START_REF] Delfosse | Structural and mechanistic insights into bisphenols action provide guidelines for risk assessment and discovery of bisphenol A substitutes[END_REF].

Peroxysome proliferator activated receptor 

PPARs are involved in the regulation of glucose, lipid, and cholesterol metabolism in response to fatty acids and their derivatives, eicosanoids, and drugs used in the treatment of hyperlipidemia and diabetes. The PPAR subfamily contains three members known as PPAR, PPAR, and PPAR.

Each PPAR subtype shows a distinct tissue distribution and ligand preference.

PPAR is highly expressed in adipose tissue, and is a central regulator of lipid storage and adipocyte gene expression and differentiation (Tontonoz, 1995) and is involved in various pathophysiologic disorders, including metabolic disease, insulin resistance, and diabetes [START_REF] Rosen | PPARgamma : a nuclear regulator of metabolism, differentiation, and cell growth[END_REF]. PPAR is the target for antidiabetic agents of the thiazolidinedione class, which includes troglitazone, pioglitazone, and rosiglitazone.

The LBD of PPAR is rather large and the diversity of ligands that can be accommodated within its pocket, mainly presented by lipid derivatives, may contribute to the large array of roles that have been assigned to PPAR.

PPAR activity of bisphenols

There is consistency between the large PPAR ligand binding pocket and the capacity to bind various compounds. Several reports have showed PPAR activation by environmental pollutants such as organotins used as agricultural fungicides and anti-fouling agents in ship paints, phthalates as well as perfluorooctane-based chemicals found in industrial surfactants [START_REF] Bility | Activation of Mouse and Human Peroxisome Proliferator-Activated Receptors (PPARs) by Phthalate Monoesters[END_REF][START_REF] Grun | Endocrine-disrupting organotin compounds are potent inducers of adipogenesis in vertebrates[END_REF]Takacs, 2007). In two recent studies (Riu, 2011a;[START_REF] Riu | Characterization of novel ligands of ERalpha, Erbeta, and PPARgamma: the case of halogenated bisphenol A and their conjugated metabolites[END_REF] we investigated the capability of the flame retardants TBBPA and TCBPA, of their biotransformation products and of their lower molecular weight analogues formed in the environment to activate PPARγ. The activity of the different compounds was studied using reporter cell lines expressing PPARs. None of the compounds tested significantly impacted PPAR or PPAR activity. In contrast, both TBBPA and TCBPA were capable of activating partially PPARγ, despite being approximately 100-fold less potent (EC50 values in the M range) than the reference pharmaceutical compound rosiglitazone (EC50 values in the 10 nM range). We also demonstrated that TBBPA and TCBPA are human, zebrafish and xenopus PPAR ligands while rosiglitazone does not bind zebrafish PPAR. This work also provides evidence that activation of PPAR depends on the halogenation degree of BPA analogues. The bulkier halogenated BPA analogues, the greater their capability to activate PPAR.

In addition, using PPARγ-based affinity column and crystallographic analysis, we clearly demonstrated that the sulfation pathway, usually considered as a detoxification process, leads for TBBPA and TCBPA, to the formation of sulfate conjugates which possess a residual PPARγ binding activity [START_REF] Riu | Characterization of novel ligands of ERalpha, Erbeta, and PPARgamma: the case of halogenated bisphenol A and their conjugated metabolites[END_REF].

Structural basis of halogenated bisphenols action on PPARγ

Despite the fact that the halogenated bisphenols are structurally unrelated to known PPARγ ligands, the crystal structures of TBBPA and TCBPA bound to the PPARγ LBD (Figure 4A) revealed the canonical tertiary fold of agonist-bound NHR LBDs [START_REF] Bourguet | Nuclear receptor ligand-binding domains: threedimensional structures, molecular interactions and pharmacological implications[END_REF]Riu, 2011a). The TBBPA and TCBPA complex structures are indistinguishable with a rmsd value of 0.29 Å for superimposed alpha carbons and nearly identical to that of PPARγ in complex with the agonist rosiglitazone [START_REF] Nolte | Ligand binding and co-activator assembly of the peroxisome proliferator-activated receptor-[gamma][END_REF] with an rmsd value of 0.62 Å. PPARγ displays a large LBP that extends from the Cterminal helix H12 to the β-sheet S1/S2 so that halogenated BPA occupy a small portion of the LBP.

Whereas rosiglitazone occupies a region of the LBP spanning from H11/H12 to the β-sheet S1/S2, TBBPA and TCBPA occupy only the region between H3 and the β-sheet S1/S2, with one of its phenol cycle nestled between H3 and the β-sheet (Figure 4B). In contrast with rosiglitazone, a consequence of their smaller size is that halogenated BPA do not interact directly with H12. A close look at the LBP shows that the phenol groups of the BPA derivatives are involved in hydrogen bonds with S342 (β-sheet S1/S2) on one side and Y473 from H12 through a water-mediated hydrogen bond network on the other side. TBBPA and TCBPA contain four halogen atoms that contribute to ligand binding through van der Waals interactions. Additional interactions involving the ligand backbone are also observed. Interestingly, comparison of human, mouse and zebrafish PPARγ sequences reveals several residue differences which could explain the differential ligand specificity of the various species. In particular the replacement of human PPARγ G284 and C285 by larger serine and tyrosine residues in zebrafish PPARγ provides a rationale for the weak binding affinity of rosiglitazone for this receptor as compared to that observed for the human homolog. In contrast, the different binding mode of halogenated compounds allows both human PPARγ and zebrafish PPARγ to accommodate TBBPA and TCBPA. The structure of PPARγ LBD bound to the metabolite TBBPA-sulfate has been also solved [START_REF] Riu | Characterization of novel ligands of ERalpha, Erbeta, and PPARgamma: the case of halogenated bisphenol A and their conjugated metabolites[END_REF]. Overall, the structure of PPARγ LBD is identical when bound to TBBPA or TBBPA-sulfate, with an rmsd value of 0.24 Å for superimposed alpha carbons (Figure 4C). The ligand is positioned almost identical to that of TBBPA, the sulfate group pointing towards H11/H12. Interestingly, accommodation of the sulfate group by PPARγ does not require any conformational change of the surrounding residue side chains.

In this orientation, the sulfate moiety fills a portion of the ligand binding pocket occupied by water molecules in the TBBPA structure and is potentially involved in hydrogen bonds with Y327, K367, H449, Q286 and S289. The presence of a conserved water molecule mediates the indirect interaction between TBBPA-sulfate and PPARγ helix H12. Overall, the crystallographic data validate the notion that this TBBPA metabolite is a PPARγ ligand with partial agonistic profile.

V. Thyroid receptors

Thyroid hormones (THs) are essential for the normal development, growth, and metabolism of all vertebrates (Zoeller, 2002), playing a major role in neurogenesis and brain function at all stages of development [START_REF] Bernal | Thyroid hormone receptors in brain development and function[END_REF]. They are produced by the thyroid. THs, namely tetra-iodothyronine (thyroxine or T4) and tri-iodothyronine (T3) are the principal representative of circulating THs. In target cells, T4 is converted in T3 which is the most active TH. Moreover, THs are key developmental and differentiation hormones in all organs of the body, including the central nervous system and the skeleton. In amphibians, THs peak at birth and parallel metamorphosis that is totally dependent upon T3 [START_REF] Leloup | La triiodothyronine, hormone de la métamorphose des amphibiens[END_REF]. The functions of THs are mediated by several isoforms of nuclear thyroid receptors, TRα and TRβ. The tissue distributions of TRs are relatively ubiquitous and the expression of these proteins begins early in development (Zoeller, 2002).

TRs activity of bisphenols

Several articles report in vitro studies revealing that BPA and its halogenated derivatives can alter thyroid hormone action by inhibiting T3 binding to and activation of TRs in the 1-10 M concentration range [START_REF] Freitas | Detection of thyroid hormone receptor disruptors by a novel stable in vitro reporter gene assay[END_REF][START_REF] Moriyama | Thyroid hormone action is disrupted by bisphenol A as an antagonist[END_REF]Sun, 2009). Halogenated BPAs share more structural similarities with TH than BPA which could explain why in certain studies, TBBPA and TCBPA were found active at lower concentrations than BPA [START_REF] Fini | Parallel biotransformation of tetrabromobisphenol A in Xenopus laevis and mammals: Xenopus as a model for endocrine perturbation studies[END_REF]. Halogenated BPAs were also shown to bind to transthyretin (TTR), the carrier protein for T4 [START_REF] Meerts | Potent Competitive Interactions of Some Brominated Flame Retardants and Related Compounds with Human Transthyretin in Vitro[END_REF], and their in vivo effects on thyroid signaling have been often observed in amphibians [START_REF] Fini | An in vivo multiwell-based fluorescent screen for monitoring vertebrate thyroid hormone disruption[END_REF][START_REF] Jagnytsch | Effects of tetrabromobisphenol A on larval development and thyroid hormone-regulated biomarkers of the amphibian Xenopus laevis[END_REF]Shi, in press;[START_REF] Veldhoen | Exposure to tetrabromobisphenol-A alters TH-associated gene expression and tadpole metamorphosis in the Pacific tree frog Pseudacris regilla[END_REF].

VI. Pregnan X receptor

PXR is a broad-specificity sensor playing a critical role in the regulation of phase I (CYP), phase II (conjugating) and phase III (ABC family transporters) detoxifying enzymes, co-ordinately regulating steroid, drug, and xenobiotic clearance in the liver and intestine [START_REF] Orans | The nuclear xenobiotic receptor pregnane X receptor: recent insights and new challenges[END_REF]. Activated PXR binds to gene promoters as a heterodimer with RXR and induces the expression of target genes such as CYP3Aand CYP2B6. This receptor plays a prominent role as protector of the endocrine system from chemical perturbation by sensing increases in the concentration of a multitude of EDCs and inducing detoxification pathways to prevent other NHRs from interactions with these chemicals.

Activation of PXR can be positive, as it accelerates the detoxification process and consequently the elimination of xenobiotics. In contrast, the premature metabolism of active compounds such as hormones or drugs means that target responses will not be activated and can lead to harmful effects or adverse interactions. The metabolism of inactive compounds can also lead to the synthesis of active metabolites, such as the transformation of methoxychlor by CYP2C11, a PXR-induced enzyme, into HPTE, a compound sharing structural similarity with bisphenol-A [START_REF] Mikamo | Endocrine disruptors induce cytochrome P450 by affecting transcriptional regulation via pregnane X receptor[END_REF].

Overall, it is difficult to conclude whether the xenobiotic activation of PXR is predominantly negative or positive, but clearly PXR plays an essential role in endocrine disruption [START_REF] Di Masi | Nuclear receptors CAR and PXR: Molecular, functional, and biomedical aspects[END_REF].

Pregnan X activity of bisphenols

Unlike most NHRs that tend to be specialized to bind few ligands with structural homologies, PXR is able to bind a large number of structurally diverse ligands with a wide range of affinities.. Human PXR binds a multitude of drugs such as the antibiotic rifampicin, the anti-cancer taxol, the anti-cholesterol SR12813, the barbituric Phenobarbital, the St John"s Wort anti-depressor hyperforine and many more, recently reviewed in [START_REF] Di Masi | Nuclear receptors CAR and PXR: Molecular, functional, and biomedical aspects[END_REF]. Furthermore, numerous studies have focused on its ability to bind environmental compounds, such as pesticides [START_REF] Lemaire | Identification of new human pregnane X receptor ligands among pesticides using a stable reporter cell system[END_REF], polychlorinated biphenyls [START_REF] Jacobs | Lignans, bacteriocides and organochlorine compounds activate the human pregnane X receptor (PXR)[END_REF]Tabb, 2004), brominated flame retardants [START_REF] Pacyniak | The flame retardants, polybrominated diphenyl ethers, are pregnane X receptor activators[END_REF], antimicrobial triclosan [START_REF] Jacobs | Lignans, bacteriocides and organochlorine compounds activate the human pregnane X receptor (PXR)[END_REF] or natural and synthetic estrogens [START_REF] Jacobs | Lignans, bacteriocides and organochlorine compounds activate the human pregnane X receptor (PXR)[END_REF][START_REF] Mnif | Estrogens and antiestrogens activate hPXR[END_REF][START_REF] Xue | Crystal structure of the pregnane X receptor-estradiol complex provides insights into endobiotic recognition[END_REF] and among them, BPA in the 1-10 M concentration range [START_REF] Jacobs | Lignans, bacteriocides and organochlorine compounds activate the human pregnane X receptor (PXR)[END_REF][START_REF] Mnif | Estrogens and antiestrogens activate hPXR[END_REF][START_REF] Sui | Bisphenol A and its analogues activate human pregnane X receptor[END_REF]Takeshita, 2001;[START_REF] Xue | Crystal structure of the pregnane X receptor-estradiol complex provides insights into endobiotic recognition[END_REF]. Interestingly, [START_REF] Sui | Bisphenol A and its analogues activate human pregnane X receptor[END_REF] found that BPA activated human PXR but not mouse PXR. Furthermore, they also showed that two others bisphenols, BPB and BPAF, are active on human PXR.

VII. Conclusions

Exposure to BPA is highly suspected to cause adverse effects in humans but controversy remains about its mechanism of action and low dose effects. Though ERα and ERβ are primary targets of BPA, alterations of other signalling pathways are probably implicated in the endocrine-disruptive effects of bisphenols. In particular, other members of the NHR family, including AR, ERRγ, PPARγ, TRs and PXR have been shown to correspond to secondary targets of bisphenols and crystallographic and modelling studies have provided structural insights as to how BPA and congeners interact with these NHRs. In addition, recent studies have revealed additional BPA targets through which bisphenols can stimulate rapid cellular responses at very low concentrations. These include the membrane-associated ERα and β (Alonso-Magdalena, 2012) and the G protein-coupled receptor 30 (GPR30) [START_REF] Chevalier | Bisphenol A promotes testicular seminoma cell proliferation through GPER/GPR30[END_REF]. These two types of receptors are capable of mediating the nongenomic effects of estrogens and xenoestrogens (reviewed in [START_REF] Wetherill | In vitro molecular mechanisms of bisphenol A action[END_REF]) and it is now widely accepted that BPA not only has the efficacy of estradiol but is also equally potent regarding several of its effects [START_REF] Alonso-Magdalena | Bisphenol-A acts as a potent estrogen via non-classical estrogen triggered pathways[END_REF][START_REF] Chevalier | Bisphenol A promotes testicular seminoma cell proliferation through GPER/GPR30[END_REF][START_REF] Wetherill | In vitro molecular mechanisms of bisphenol A action[END_REF]. Thus is conceivable that BPA could act in a synergistic way through simultaneous action on various nuclear and membrane-associated receptors. Moreover, most of our current knowledge of BPA action is based on single molecule exposure in model systems in vitro or in vivo. These efforts have therefore taken little account of a more realistic situation in which humans are chronically exposed to low doses of multiple EDCs which very likely act also in a synergistic manner.

Both biological and structural data on EDC interactions with nuclear and membrane receptors, in addition to enable a better understanding of EDC activities will provide guidelines for the development of safer substitutes devoid of hormonal activity and may help environmental risk assessment. Alternatively, they will have potential applications in drug discovery by revealing unforeseen binding mechanisms.

VIII. Acknowlegments

IX.

Zoeller, T. R., Dowling, A. L., Herzig, C. T., Iannacone, E. A., Gauger, K. J., Bansal, R. (2002).

Thyroid hormone, brain development, and the environment. Environ. Health Perspect. 110 Suppl 3, 355-361.

Figures Tables

  This work was supported by Programme National de Recherche sur les Perturbateurs Endocriniens (P.B.), Agence Nationale de Recherches Contaminants, Ecosystèmes, Santé Project "BISCOT" 2010 Contaminants et Environnements: Métrologie, Santé, Adaptabilité, Comportements et Usages 004 02 (to P.B. and W.B.) and Programme Environnement Cancer Project "SynerPXR" 2012 (to P.B. and W.B.).

Figure ER :

 ER Figure ER: Two different binding modes of BPs. (A) The whole structure of the ERα LBD in complex with

Figure ERR :

 ERR Figure ERR: Structural determinants of BPs recognition by ERRs. (A) Overall structure of unliganded ERR

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