Chengcheng Wang

Harold Mouchère
email: harold.mouchere@univ-nantes.fr

Aurélie Lemaitre
email: aurelie.lemaitre@irisa.fr

Christian Viard-Gaudin
email: christian.viard-gaudin@univ-nantes.fr

Online Flowchart Understanding by Combining Max-margin Markov Random Field with Grammatical Analysis 1

come

symbols and can expand their styles freely. One typical example of such diagram is flowchart, which makes the illustrations of programs or structural objects very intuitive. With the emergence of electronic devices, the situations are becoming more common that people have to record their diagrams in their tablets and hopefully, the applications would facilitate the process of diagram parsing. Understanding and processing diagrams by machine learning techniques is also becoming a hot research topic, and fortunate enough, as a 2D handwritten language, the task of recognizing sketched diagram is similar to recognizing handwritten mathematical expressions and the latter can be referenced.

A traditional workflow of parsing 2D handwritten language is a trilogy: grouping strokes into symbols, recognizing symbols, and then analyzing structures [START_REF] Chan | Mathematical expression recognition: a survey[END_REF]. We can follow this process in diagram recognition in a broad way, however, the properties differ from one specific 2D language to another. Cases are rare that one symbol is contained in another except square root operator in mathematical expressions, but it is common in flowchart that texts are contained in terminal nodes. Sketched diagrams also have a more flexible grammar in that they can almost expand their symbols in all directions, but in mathematical expressions, rules are settled so that there is less variability. From Figure 1 we can see that arrows in a flowchart can have various shapes, and can point to almost everywhere. Flowchart also cover a larger scope than mathematical expressions [START_REF] Chan | Mathematical expression recognition: a survey[END_REF][START_REF] Mouchère | Advancing the state of the art for handwritten math recognition: the crohme competitions, 2011-2014[END_REF]. All these add difficulties in sketched diagram recognition.

Although most of the 2D handwritten languages can be interpreted as the trilogy that has been mentioned above, recent researches tend to use a global method to avoid the propagation of errors, which decrease the recognition rate by feeding the misinterpreted symbols or structures into the following steps [START_REF] Chan | Mathematical expression recognition: a survey[END_REF][START_REF] Mouchère | Advancing the state of the art for handwritten math recognition: the crohme competitions, 2011-2014[END_REF]. Instead of enlarging the search space by generating several segmentations and several symbol hypotheses, our proposal is to guide the local recognition using neighborhood information. In this way, the problem is not solved by simply performing classification of individual component, that approach does not take into account the empirical fact that labels do not occur independently; instead, each label displays a strong conditional dependence on the labels of the surrounding components. To this end, document is arranged as a structured object, which can fit into an undirected graphical model, or more specifically, a Markov Random Field (MRF). A MRF that would incorporate local, neighborhood and global information would be a superior solution to solve symbol ambiguity problems. In addition, it is possible to train this model in a structured learning framework. Two alternatives exists for parameter learning: logistic loss based Conditional Random Field (CRF) approach and hinge-loss based structured SVM approach. CRF is almost intractable for general graphical models [START_REF] Koller | Probabilistic graphical models: principles and techniques[END_REF] [START_REF] Nowozin | On parameter learning in crf-based approaches to object class image segmentation[END_REF], as shown in Figure 2. Meanwhile, several works [START_REF] Joachims | Training linear svms in linear time[END_REF] [START_REF] Hui Teo | A scalable modular convex solver for regularized risk minimization[END_REF] showed that structured SVMs avoid the inference in the whole label space by a heuristic search in a primal form, making the learning tractable. This paves a new way of learning parameters of MRF, and due to its max-margin property of its loss function, the structural SVM can lead to a Max-Margin Markov Random Field (M3N).

In this work, we adopted structured SVM learning methods and MRF for the first time in the field of 2D handwriting recognition, leading to a novel statistical and structural information combined online flowchart recognition method, which is also applicable to other 2D handwriting problems. We build a M3N on the stroke level of the online flowcharts for stroke labeling. The parameters of M3N are learned using structured SVM. After stroke labeling, we use a grammatical description language extended from a previous work [START_REF] Lemaitre | Interest of syntactic knowledge for on-line flowchart recognition[END_REF] to parse the structure of a given sketched diagram, thus obtaining the final recognized flowchart. In order to fully evaluate of the recognition process, the ground-truth of the flowchart dataset [START_REF] Awal | First experiments on a new online handwritten flowchart database[END_REF] have been completed by adding the object relations.

In the following sections, we first have a review of previous works on 2D handwritten language recognition and the application of structured learning, especially CRF and structured SVM, and how they inspired our handwriting recognition research. In the third section, we will describe the stroke labeling problem, in which a full description of our max-margin MRF building and training will be given. In the fourth section, we explain how the strokes labels are used in the syntactical analysis. The experiment will be given in the fifth section after a short description of the new version of the evaluation dataset. We will conclude the research in the sixth section.

Related researches

Flowchart can be viewed as one type of 2D handwritten languages. To enlarge the scope, we will review more generally 2D handwritten language recognition researches that complete symbol recognition and structure recognition simultaneously. Integrating neighborhood information in handwritten document understanding can be done globally by using strict language modeling like grammars or more locally through CRF or alternatively with structured SVM. Both kinds of approaches will be discussed in this section.

2D Handwritten language recognition

Significant research effort has been reported for recognition of math expressions in the recent years [START_REF] Mouchère | Advancing the state of the art for handwritten math recognition: the crohme competitions, 2011-2014[END_REF], in part due to online input devices becoming more popular. Zanibbi et al. [START_REF] Zanibbi | Recognizing mathematical expressions using tree transformation[END_REF] proposed baseline structure tree that parses the elements of a mathematical expression into a tree that fits natively its structure and then passed it to lexical parser and expression analyzer. The output of this three-pass system is an operator tree that can Fig. 2 Examples of graphical models. MRF and CRF share the same graphical models, but MRF are generative models which model the joint probability distribution, while CRF are discriminative models which model the conditional probability distribution. The black triangles on the edges are the unary factor nodes, while black squares on edges are the pairwise factor nodes.A linear chain model (left example) will be easier to train and will be used for inference with respect to a general model which contains cycles (right example).

be interpreted by computer. In [START_REF] Tapia | Recognition of online handwritten mathematical expressions using a minimum spanning tree construction and symbol dominance[END_REF], a minimal spanning tree (MST) is used to arrange all strokes into a graph and used symbol dominance information to set the weights of the tree so that they take into account the baseline of the mathematical expression. Symbol relation tree (SRT) is used in [START_REF] Heon | Efficient search strategy in structural analysis for handwritten mathematical expression recognition[END_REF], it overcomes the baseline restrictions and build the tree using dominance symbol. They also used layered search to include symbol hypothesis and prune search space. These elegant solutions are well adapted for mathematical expressions, however, they might not be applicable to flowcharts or other sketched diagrams as the concepts baseline and dominance symbol are too specific. Another drawback of these approaches is their greedy decisions. In order to take the final decisions as later as possible, Awal et. al. [START_REF] Awal | A global learning approach for an online handwritten mathematical expression recognition system[END_REF] used a 2D dynamic programming algorithm symbol hypothesis generator, concatenating it with a Time Delayed Neural Network (TDNN) [START_REF] Waibel | Phoneme recognition using time-delay neural networks[END_REF] symbol classifier. Besides, structure interpretation also suffers from ambiguity, which is caused by the ambiguous position of symbols and previous recognized symbols. Symbol relation tree is proposed in [START_REF] Heon | Efficient search strategy in structural analysis for handwritten mathematical expression recognition[END_REF] to include all the symbol hypothesis and relation hypothesis. They used a heuristic measure to calculate the cost of a certain tree and they get the interpreted mathematical expression by best-first-searching for the interpretation with the lowest cost. Hence, this tree-style models may not be applicable to our diagram recognition needs.

There are no public flowchart or any other sketch diagram dataset until 2011 [START_REF] Awal | First experiments on a new online handwritten flowchart database[END_REF], and after that, many researches appeared to improve that first trial research. Lemaitre et. al. [START_REF] Lemaitre | Interest of syntactic knowledge for on-line flowchart recognition[END_REF] analyzed the structure of the flowchart and described them in DMOS (introduced in section 4.1), a grammatical method for structured document analysis. This approach provides a global solution to the problem. The structure, symbol and stroke labels are recognized in one step. However, this unified recognition framework did not use any statistical learning methods. To improve this method, research combined statistical and structural information [START_REF] Carton | Fusion of statistical and structural information for flowchart recognition[END_REF]. They used deformation scores to measure potential of candidate symbols so that they could dynamically switch to a preferable symbol in the structured search. However, the proposed approach did not cover simply all the possible variations to build a given symbol. For instance, the drawing of a rectangle can be done in a single stroke or can be done with 4 strokes, one side at a time. To deal with this variability, the structural approaches need to define one specific rule for specific case. Wu et.al. [START_REF] Wu | Offline sketch parsing via shapeness estimation[END_REF] proposed to recognize symbols in flowcharts by using shapeness, which is a property of whether a symbol has a good shape. They used a 256 dimensional feature and represented it compactly by using 16 INT64 numbers, calling it INT64 feature. The INT64 feature is used in a linear classifier to filter out symbols with good shape, then a neural network is used to achieve the final recognition. This research outperforms others due to its separation of processing of symbols according to whether they are having a regular appearance, this is too specific to the field of flowchart recognition: for mathematical expression recognition, there are less texts and symbols have regular shapes, and the position relationship between texts and symbols are more complicated.

Bresler et.al. proposed max-sum model in [START_REF] Bresler | Modeling flowchart structure recognition as a maxsum problem[END_REF], which can be viewed as a structured model incorporating unary and pairwise relationships. Their max-sum model tried to maximize the global compatibility of symbols. They first extracted a bunch of symbol candidates (about 8.8 times the groundtruth symbol set size) and evaluated their combinations to find the most suitable symbols that fit in the flowcharts. They formulated the max-sum model as a an Integer Linear Programming (ILP) [START_REF] Roth | Integer linear programming inference for conditional random fields[END_REF] problem and solved it using IBM ILOG CPLEX 1 .

In their following research [START_REF] Bresler | Recognition system for on-line sketched diagrams[END_REF], they refined their research by carefully dealing with text and arrow symbols: they first filtered out text by using Bi-directional Long-Short Term Memory neural network (BLSTM) based Bayesian classifiers then checked connection points of each symbol to decide the connecting arrows. They also published finite automata dataset to validate their research. One of the inspirations of their effort to our research is that their max-sum model is an attempt to include the global information in one model. Though achieving high recognition precision, filtering of text and their effort in deciding arrow type make their effort too specific to flowchart. Besides, the large amount of generated symbol hypothesis increased the inference effort in the max-sum model, and will always inevitably drop some true symbols.

Structured learning

Structured learning describes a wide range of problems that involve structured objects instead of scalar discrete or real values. By denoting X an input space, and Y an output space, the structured learning means fitting a function h to map from X to Y using a set of training samples in (X × Y). By using the word structured, the output Y should be arranged in a structured manner, like trees or graphs. The task of stroke labeling in flowchart recognition corresponds to this description as the underlying strokes are arranged in a Markov random field. Here we have a review of previous researches that used CRF and M3N, two practical forms in structured learning [START_REF] Nowozin | Structured learning and prediction in computer vision[END_REF].

As we have mentioned before, CRF is a powerful tool in describing regional context. Research utilized Bayesian CRF in their flowchart recognition [START_REF] Qi | Diagram structure recognition by bayesian conditional random fields[END_REF]. They first modeled the distribution of parameters, pairwise probability and the inverse of partition function as Gaussian distributions, and then they repeatedly trained the model by minimizing Kullback-Leibler divergence between the new and the original models. This method is called expectation propagation. They did their research on text-free segment based flowchart recognition. However, Gaussian distribution is a strong assumption that may not applicable to pairwise potentials. Besides, their research did not continue with symbol recognition and their flowchart contains much fewer symbol types compared to the flowchart dataset mentioned in [START_REF] Awal | First experiments on a new online handwritten flowchart database[END_REF], only arrows and nodes are included.

1 www.ibm.com/software/products/en/ibmilogcpleoptistud A promising result using CRF in sketch diagram recognition is described in [START_REF] Delaye | Contextual text/non-text stroke classification in online handwritten notes with conditional random fields[END_REF], though it is originally designed for text/nontext classification in handwritten documents. They build the CRF using a set of associative potential functions and interactive potential functions, the latter are built on a set of 5 relations, not limited to spatial, temporal and touching relations. In their later research [START_REF] Delaye | Multi-class segmentation of free-form online documents with tree conditional random fields[END_REF], they further improved labeling accuracy by building a hierarchical tree-CRF, on the same handwritten document database, and they classify strokes to five classes, which is more specific than just text/nontext. They grouped and recognized symbols by building a MST on the recognized strokes of the same type. However, the hierarchical tree-CRF's performance is largely controlled by the clustering distance threshold, which is specific to the document and can largely affect CRF's performance according to their experiment.

On the other hand, M3Ns are showing promising performance in the field of image labeling. The property that CRF can be reduced to a structured SVM [START_REF] Joachims | Training linear svms in linear time[END_REF] [30] provides smooth transition from traditional research of CRF to max-margin MRF representation. One example is [START_REF] Pei | Efficient semantic image segmentation with multi-class ranking prior[END_REF], which uses M3N to combine multiple local beliefs of superpixels and regional affinity. They also used global constraints to refine unary potentials. Structured SVM has also been applied in the field of object location [START_REF] Matthew | Learning to localize objects with structured output regression[END_REF], point matching [START_REF] Smola | Robust near-isometric matching via structured learning of graphical models[END_REF] and pose esti-mation [START_REF] Ferrari | Progressive search space reduction for human pose estimation[END_REF]. However, one common idea behind the construction of M3N is that unary potentials should describe the local belief based only on the local observation, while pairwise potentials, or even higher order potentials should describe regional interactions.

Regarding all the previous researches using MRF in handwriting recognition [START_REF] Zhu | On-line handwritten japanese characters recognition using a mrf model with parameter optimization by crf[END_REF] [11] [START_REF] Delaye | Multi-class segmentation of free-form online documents with tree conditional random fields[END_REF], MRF has shown to be a powerful structured model to describe neighborhood information. We discarded the idea of finding a tree-structure in the representation of sketched diagrams and resort to general graph MRF that may contain cycles to capture neighborhood relationship between strokes. Training by structured SVM learning algorithm is a natural solution to avoid the intractable learning problem in the partition function of CRF that may contains loops in underlying graph [START_REF] Koller | Probabilistic graphical models: principles and techniques[END_REF]. Training a M3N consists of learning the unary potentials and the pairwise potentials to incorporate local belief and neighborhood compatibility accordingly. With the labeled strokes, the grammar parsing will result in a legitimate, reasonable diagram. This is the first attempt to use structured SVM in 2D handwritten language recognition, and the combination of structural grammars and statistical recognition result gives a complete comparable referral on different recognition stages.

3 Stroke labeling using max-margin MRF Suppose we have N diagrams, then we denote the stroke observation set as X (n) for each diagram, which is indexed by n. We denote strokes X

(n) 1 , X (n) 2 , . . . , X (n)
Mn = X (n) that belong to the observation set. M n is the number of strokes in an observation set. The topic of this section is stroke labeling problem, so each of the stroke observation has a corresponding label Y (n) i , which takes discrete labels such as Arrow, Terminal and so on, depending on the diagram. In the following, in case of no ambiguity, we simply define the observation set of a specific sample of diagram X and its corresponding label set as Y, each strokes will be indexed by subscripts.

Classically, we use an energy function to describe the whole compatibility of the flowchart. It is composed of a set of unary energy functions and pairwise energy functions:

E(X, Y) =   i (X i , Y i ) + <i,j>∈E (X i , X j , Y i , Y j )   (1)
In the energy function in equation ( 1), the unary energy function describes the local belief Y i given only the isolated observation X i . The pairwise energy function (X i , X j , Y i , Y j ) provides regional compatibility. In many image segmentation researches, pairwise energy functions try to fix the local belief by smoothing regional labels given the regional observations. That energy function, under the assumption of Gibbs distribution [START_REF] Koller | Probabilistic graphical models: principles and techniques[END_REF], can be incorporated into a MRF:

P (X, Y) = exp [-E(X, Y)] = i e -(Xi,Yi) <i,j>∈E e -(Xi,Xj ,Yi,Yj ) = i Φ(X i , Y i ) <i,j>∈E Φ(X i , X j , Y i , Y j ) (2)
Here in formula (2), we use exponential form of potential function to ensure potential function are always positive, which is a requirement of MRF [START_REF] Koller | Probabilistic graphical models: principles and techniques[END_REF]. The inference problem is to solve Y = argmax Y P (X, Y), which can also be interpreted in the form of energy function as Y = argmin Y E(X, Y). In the following subsections, we will describe the feature selection, inference problem and learning problem separately.

Potential functions

The potential functions should be built to exhibit the relevant features from the raw data. Here we discuss the selected features for unary potential functions and pairwise potential functions, then describe the mathematical expressions.

Raw feature selection

Considering that diagrams drawn by different people have different scales, as a preprocessing step, we rescaled all the diagrams to a [-1, 1] bounding box and kept its height/width ratio. For the convenience of uniform feature extraction, we sampled each stroke to equal count of points with a constant spatial step. Our trial on the number of points per stroke showed that the denser the sampling the better the feature extraction ability, but performance is hard to improve after 30 points per stroke. For the balance between performance and processing time complexity, we set sampling point on each stroke to 30.

To extract raw features for unary potential functions Φ(X i , Y i ), we calculate the ∆x, ∆y, cos θ, sin θ, cos γ, sin γ on each sampling point as illustrated with Figure 3. The angle θ is the slope angle on the current Fig. 3 This graph illustrates raw features for unary potentials. i and i + 1 are two consecutive sampled points on a stroke, and we here showed features ∆x, ∆y, θ and γ for sampled point i.

point, and γ i = θ i+1 -θ i = ∆θ. This describes the curvature of that point. For the ∆x, ∆y, we normalize them by dividing the width and height of the bounding box of the flowchart separately. Altogether there are 30 × 6 = 180 features that describe a stroke, and we normalize them by dividing by the maximum absolute value of each component.

The pairwise potentials Φ(X i , X j , Y i , Y j ) should describe the regional compatibility of label Y i , Y j given observation X i , X j . We focus on two types of neighborhood in pairwise function: temporal neighborhood and spatial neighborhood. Hence, from the time domain, X i and X i+1 are considered as neighbors, so there is a potential function that describes their affinity. For the spatial neighborhood, we define a threshold distance. If the stroke pairs' minimal distance is below that threshold, they are considered as neighbors. To decide the threshold, we tested thresholds from 0.01 to 0.07 and evaluated stroke labeling accuracy and training time, and we took 0.03 as a preferable threshold in the following experiments. The detail of this spatial threshold decision can be referred in section 5. The pairwise potential function is undirected, which means Φ(X i , X j , Y i , Y j ) is equivalent to Φ(X j , X i , Y j , Y i ). The Figure 4 shows an example of sketch with its set of unary and pairwise potential functions. We extract raw features for pairwise potentials by finding the displacement of each of the sampled points on one stroke to the point on another stroke that can offer the minimal distance. As shown in Figure 5, X 1 is the first sampling point on the left stroke, and from all the sampling points on the right stroke, Y n has the minimal distance. The displacement from X 1 to Y n is shown by a dotted arrow, and this displacement generates ∆x and ∆y as two pairwise raw features. For the sampling points Y 1 on the right stroke, we find the sampling point X 1 on the left stroke with minimal distance. We do this repeatedly on every sampling points of each pair of strokes. Altogether, there are 30 × 2 × 2 = 120 pairwise raw features. In many researches on analyzing online handwritten documents, researchers would chose manually selected and refined features to feed the classifiers [START_REF] Delaye | Multi-class segmentation of free-form online documents with tree conditional random fields[END_REF]. We, however, simply selected very raw features as described above, and then use supervised classifiers to classify them to different types of stroke relationships, and the feature derived from the classification result is used as feature. In this way researchers avoided the effort to manually select different features according to different scenarios, making our method adaptable to fields beyond flowchart. However, domain specific raw features could have better results.

Mathematical formulation of potential functions

The unary potential function Φ(X i , Y i ) can be formally defined according to equation [START_REF] Awal | A global learning approach for an online handwritten mathematical expression recognition system[END_REF].

Φ(X i , Y i ) = exp - L l=1 1 Yi=l K k=1 w k,l f k (X i ) = exp - K k=1 L l=1 w k,l [1 Yi=l f k (X i )] (3)
In the equation above, 1 Yi=l is the indicator function given the current label, and K is the number of features that are fed in this unary potential function. L is the number of possible labels. In this research, since unary potential functions are to describe the local confidence of a label, we should use a supervised classifier that gives confidence on final labels directly. Practically, all classifiers giving this kind of outputs could be used. Since raw features directly reflects the property of strokes which are of various shapes, and even same type of stroke is having various shapes in flowchart, we choose ensemble methods to improve robustness of the feature extraction. We selected random forest [START_REF] Breiman | Random forests[END_REF], which uses averaging methods to combine different decision trees to prevent over-fitting, and GBDT [START_REF]Artificial Intelligence Group of Microsoft Research Asia[END_REF], which is using boosting to combine several weak classifier to a strong one. The refined features are the probability of each label given the observation. Both classifiers give the probability of predicted class, and here we concatenated them to form refined feature. Since the f k (X i ) describe the probability of different labels based on two pre-trained classifiers, K = 2 × L. The classifiers are trained on raw features of observations.

Following the idea of unary potential functions, the formulation of pairwise potential functions in equation 4 also used an indicator and a feature descriptor.

Φ(X i , X j , Y i , Y j ) = exp   - l1,l2∈L l1=1,l2=1 1 Yi=l1,Yi=l2 K k w l1,l2,k f k (X i , X j )   = exp   - K k l1,l2∈L l1=1,l2=1 w l1,l2,k [1 Yi=l1,Yi=l2 f k (X i , X j )]   (4)
That feature descriptor should describe local properties that reflect local relationship of two neighboring strokes, thus completing local compatibility description. We continue using random forest and GBDT, taking pairwise raw features and classify them into given stroke relationships. For within-symbol strokes, the symbol label is used as stroke relationship label, and for intersymbol strokes, stroke relationship inherits from symbol relationship (for a concrete example, section 5.1 describes possible symbol relationships for flowchart database). By adding "no relationship" for other situations, all possible stroke relationships are included.

Though there are choices for a more sophisticated and advanced classifier, we simply disregarded the abundant choice for other researchers to push our boundary further. Whatever classifier one would use, the automatic feature extraction process from raw features to the classified class enables one to use this identical process in their own handwriting recognition task is one contribution in our work, which greatly facilitated the transplanting of our system to other problems.

Model inference

Inference problem has been a main focus of probabilistic graphical model research. Here in this research, we adopt Alpha-Expansion-Fusion algorithm [START_REF] Fix | A graph cut algorithm for higherorder markov random fields[END_REF]. This is a graph-cut based algorithm so it is faster than belief propagation. Besides, this algorithm adopts Quadratic Pseudo-Boolean Optimization (QPBO) so that its energy does not have to be submodular.

Parameter learning

In the structured SVM framework, a discriminant function F (X, Y; w) exists describing the compatibility of label Y and observation X. The dot product of the feature vector f (X, Y) and parameter w can give a good description of F (X, Y; w), in which the parse feature function reflects the property of the structured objects itself. As formulas (3) and ( 4) indicate, potential function can be reorganized in the format as exp [-w • f (X, Y )], so by aggregating (2), ( 3) and ( 4) we can get the feature vector representation and parameter vector w, expressed in formula [START_REF] Breiman | Random forests[END_REF]. Inference problem in the form of discriminant function can be expressed as Y = argmax Y F (X, Y). The MRF expression formula (2) is not a linear representation of features, however, minimizing the energy function is equivalent to maximizing the structured learning discriminant function, as shown in formula (5):

F (X, Y) = -E(X, Y) = w • f (X, Y) (5)
A solution to generalize normal SVM training to structured outputs is presented in [START_REF] Joachims | Training linear svms in linear time[END_REF]. All the things to do in training is to find a cutting-plane, described by w, that separates right labels from those inferred by the models but with wrong labels. In this research, we use margin-scale problem formulation and solve the problem by using one-slack structural SVM learning algorithm [START_REF] Joachims | Cutting-plane training of structural svms[END_REF]. The problem can be formulated as follows:

min 1 2 ||w|| 2 + Cξ, (6)
with the constraints

1 N N i=1 ∆(Y (i) , Ȳ(i) ) -w • f (X (i) , Y (i) ) -f (X (i) , Ȳ(i) ) ≤ ξ ∀( Ȳ(1) , Ȳ(2) , . . . , Ȳ(N) ) ∈ Y N . (7)
In formula ( 7) Ȳ(i) is the predicted labels for sample i, while the true labels is denoted as Y (i) . The structural loss ∆(Y (i) , Ȳ(i) ) defined in this loss function specifies the margin between true label and the incorrect label in our max-margin MRF training. The one common form of structural loss is Hamming distance between true labels and predicted labels, and we continue use that in this paper. The difficulty of structural SVM is that the label space Y (n) may be tremendously large: it takes L Mn possible label combinations, so the constraints in the QP may be very large, which could not be handled easily. For this problem, [START_REF] Joachims | Cutting-plane training of structural svms[END_REF] proposes N-slack and one-slack structural SVM training algorithm that uses a heuristic search strategy to add constraints dynamically. The main idea is to get the most violated instance in each iteration and to add that into constraints set W, replacing the constraints in [START_REF] Bresler | Recognition system for on-line sketched diagrams[END_REF], then solve the QP in primal space. The iteration will stop when the constraint set remains unchanged after a certain iteration. The majority of constraints are behind the most violated one, so it is unnecessary to add all the constraints. For the completeness of this paper, we repeat the algorithm in Algorithm 1.

Algorithm 1 Training Structured SVM by using margin-rescaling One-Slack formulation

Require: S = (X (1) , Y (1) ), . . . , (X (N ) , Y (N ) ) , C, 1: W ← ∅ 2: repeat 3: (w, ξ) ← Solving QP, replacing constraints [START_REF] Bresler | Recognition system for on-line sketched diagrams[END_REF] with W 4:

for all i ∈ [1, . . . , N ] do 5: Ȳ(i) ← argmax Ȳ(i) ∈Y ∆(Y (i) , Ȳ(i) ) + w • f (X (i) , Ȳ(i) )
6: end for 7:

if 1 N N i=1 ∆(Y (i) , Ȳ(i) )- w f (X (i) , Y (i) ) -f (X (i) , Ȳ(i) )
> ξ + then

8:

W ← W ∪ Ȳ(1) , Ȳ(2) , . . . , Ȳ(N) 9:

end if 10: until W unchanged during iteration

Grammatical analysis of handwritten flowcharts

Once the isolated strokes have been labeled, we propose to combine the results using a grammatical description. This second step does ensure the global consistence of the recognition. The presented system is an extension of the grammatical analysis from the previous works [START_REF] Lemaitre | Interest of syntactic knowledge for on-line flowchart recognition[END_REF] and [START_REF] Carton | Fusion of statistical and structural information for flowchart recognition[END_REF]. In this former solutions, the analysis was based only the set of atomic elements in data: the full strokes and the straight-lines (segments) within the strokes. Using these terminals, their relative layout, and the a priori lexical knowledge about flowcharts the syntactical analysis recognizes the symbols. Compared to [START_REF] Lemaitre | Interest of syntactic knowledge for on-line flowchart recognition[END_REF] this new work adds two main propositions: using pre-recognized strokes from a statistical approach (the MRF in our case) and producing the relationship labels between the recognized symbols.

The DMOS approach

The DMOS (Description and MOdification of the Segmentation) method [START_REF] Coüasnon | Dmos, a generic document recognition method: Application to table structure analysis in a general and in a specific way[END_REF] is a grammatical method for structured documents analysis. The using of the grammatical language EPF (Enhanced Position Formalism) enables a syntactic and structural description of the content of a document. From the description in EPF of a model of documents, it is possible to compile automatically an analyzer which will be used to process the documents.

The DMOS engine is based on the Prolog language. It means that a document is described with a set of rules. For example the following rule allows to build a quadrilateral object using four segments (TERM SEG) locally named S1, ..., S4. The AT(.) operator allows to add constraints on the next used terminals. For example AT(end S1) && TERM SEG S2 means that S2 should be at the end of the the segment S1. Without these constraints, a quadrilateral would be recognized for each set of four segments whatever their layout. Using this rule, it is possible to build a top rule to recognize a complex document based on several quadrilaterals. As DMOS is based on a Prolog solving engine, the analyzer can try and test, using backtracking, all combinations of segments to satisfy the main rule. The order of the rules in the grammar can have a big impact on how efficient is this search. Indeed some predicates can have to enumerate a lot of candidates. To optimize this search, the current version of DMOS is able to build and save intermediate objects (like quadrilaterals in the previous example) and then to use them as new terminals in the explanation of a full document.

The Flowchart analysis

The grammar processes the strokes in three main steps:

1. build all boxes found in the documents using [START_REF] Carton | Fusion of statistical and structural information for flowchart recognition[END_REF], 2. label the boxes and connect them with arrows, 3. use the remaining strokes to build text areas.

The second step follows a simple flowchart grammar: start with a terminator or a connection symbol, then continue with an arrow to the next box; each box (terminator, connection, process or data) is followed by an arrow which ends on a box; decision boxes are followed by two arrows; . . . The next rule illustrates in a simplified EPF language how an arrow follows a process box. This recursive predicate builds a list of symbols starting by a process named Pr (of course the real rules deal also with the other types of boxes) and an arrow named Arr. The first step is to check if the box Pr satisfies the graphical conditions to be a Process. It should be noticed that the real grammar should accept flowcharts which are not perfectly drawn. For example in Figure 10 an arrow is missing to connect the "Input n,m" box and the "r= n%m" box.

The grammar is designed to force the explanation of all available strokes. Thus if some strokes are remained at the end of the analysis and if they can not be included in a text area in the last step, then the predicate fails and thanks to the backtracking, another solution is explored.

In the previous work [START_REF] Lemaitre | Interest of syntactic knowledge for on-line flowchart recognition[END_REF] the system was based only on the syntactic description of the document based on the relative positions of the strokes. In [START_REF] Carton | Fusion of statistical and structural information for flowchart recognition[END_REF] some statistical information based on the boxes shapes are used to first detect the boxes and then, using the same structural grammar as in [START_REF] Lemaitre | Interest of syntactic knowledge for on-line flowchart recognition[END_REF], build the flowchart.

In this work the labels obtained from the MRF are used to improve the syntactical analysis at three points:

box labeling: in the first step of the analysis, if all strokes of a box have the same label, then the box will have this label, otherwise criteria from [START_REF] Carton | Fusion of statistical and structural information for flowchart recognition[END_REF] are used; arrow ending: during the third step, if a remaining stroke labeled as an arrow is close to a detected arrow, then they are merged; text detection: during the third step, the text areas start with a stroke labeled as text and then they are expanded horizontally with the unused strokes.

Experiments

We performed our sketch diagram parsing experiments on the updated publicly available dataset Flowchart Dataset [START_REF] Awal | First experiments on a new online handwritten flowchart database[END_REF].

Data description

The flowchart dataset consists of handwritten flowcharts of various complexity. Some are complex algorithms with descriptive texts while some are just simple and straightforward sequential operations. The used samples are the same as in the already published Flowchart dataset [START_REF] Awal | First experiments on a new online handwritten flowchart database[END_REF] but the ground-truth has been updated. The symbols in the flowchart dataset are divided into 7 classes: Data, Terminator, Process, Decision, Connection, Arrows and Text. Strokes inherit their belonging symbol label. Compared to the initial version, the ground-truth contains the symbol segmentation and labels but also their relationships in the flowchart. Thus, the latest version includes three directional relationships between symbols: i) Associated Text between node or arrow and their associated texts; ii) Source and iii) Target, which clarify the relationships between arrow and linked nodes. This opens the possibility for researches to utilize and recognize these relationships. The flowcharts have been collected using digital pens from university students of the research laboratory. This dataset is split into train set and test set. However, we further manually divided the training set into three folds to perform 3 fold cross-validation for parameter tunning. We divide the training set in such a way that each fold has no flowchart writers overlapped with the writers in other folders. We sacrificed the equality of each divided size for no overlapped writer, to avoid the situation where the writers' writing habits contributes to the recognition result on validation set. For the detailed statistics of flowchart dataset, please refer to Table 1.

Parameter tuning by cross-validation

Our model has several hyper-parameters to be decided, and that can be done by cross-validation using our divided 3-fold training set. Here in this subsection, we briefly explain how to decide the spatial distance threshold mentioned in 3.1.1. Spatial distance threshold would affect the graphical model's structure, and the smaller the spatial distance is, the sparser the graphical model would be, which may effect the training and inference time, and stroke labeling performance. In each round of training, we select one fold as validation set, and train on the combination of the other 2 folds. Then we take the average on each fold as current parameter's performance measure. In this research, we use pystruct [START_REF] Müller | pystructlearning structured prediction in python[END_REF] back-ended by OpenGM [START_REF] Andres | OpenGM: A C++ library for discrete graphical models[END_REF] to perform structured SVM parameter learning and M3N inference. For stroke labeling accuracy before 0.03, it is increasing steady. This is due to the fact that with larger spatial distance threshold, the more connections exist for vertices on graphical models, the richness of connection provides more information of the flowchart. However, the accuracy appears to be unstable after that because expanded edges are providing a redundancy, which is having a side effect on graphical model learning and inference. By selecting two peak values of stroke labeling accuracy and drop 0.05 which is having a longer inference time, we finally selected 0.03 as threshold value.

We use similar steps for determination of other parameters, such as the minimal number per leaf and the number of decision trees in random forest classifier, and maximal number of leaves of GBDT. Since there are too many parameters to do grid-search, we selected one type of parameters, then settle down others to perform parameter grid search by cross-validation. Then we switch to another type of parameter, until we have tuned all the parameters. Finally, the random forest has 80 trees and 14 as minimal samples per leaves and GBDT has 25 trees with a maximal 31 leaves per tree to form the unary potential function feature refiner; for the pairwise potential function feature refiner, random forest has 80 trees and 3 minimal samples per leaves and GBDT has 30 trees with a maximal 127 leaves per tree to form the refined feature generator.

Stroke recognition

After the determination of parameters, we train our model on the whole training set and perform test on test set. The first stage of our flowchart recognition system is to use M3N to determine stroke labels. Due to the randomness of random forest and GBDT, we launched 5 experiments to recognize flowchart. The average recognition result can be referred to Table 3, and we selected the experiment that has median recognition rate to illustrate the detail below. There are 7 classes of symbols in flowchart, so strokes are classified into 7 classes. Here we show the confusion matrix in Figure 7 and precision, recall and F1 score of our model in Table 2: Our M3N model is using GBDT and Random Forest as raw feature extractor, and we also tested their stroke Fig. 7 Confusion matrix for strokes labeling result on test set. The left one is the result after M3N inference but before grammatical analysis. The right one is after grammatical analysis. Each row of the matrix contains all the strokes of the groundtruth class, and each column contains all the strokes of the predicted class. The denser each block is on the diagonal, the higher the recall rate.

recognition rate along with M3N combined stroke recognition rate. From Table 3 we can see that when using a standalone classifier to classify strokes, the classifier does not use neighborhood information and it is keeping at a recognition rate a little above 80%. By combining it with M3N, we observed a significant improvement of stroke recognition rate. This validated our belief that MRF is suitable for modeling the 2D handwritten language.

From the confusion matrix before grammatical analysis, terminator class is having the lowest recall rate. That is because terminator is having a similar shape with process. Process is actually a rectangle while terminator is a rounded rectangle, there's no doubt why many strokes belonging to terminator are classified to process. Besides, they can also be misclassified to arrow because arrow is of various shape itself. Another interesting point is that text have the highest recall rate, that's mainly because text has its own style, they would Fortunately, with grammatical analysis, this biased sample problem is eased. From the right confusion matrix, which is the result after grammatical analysis, we observe an obvious decrease of error recognition case on arrow, process and data. However, there's an increase in the error where strokes are labeled as text. The class text is hard to encoded in grammatical rules so our grammatical analysis process fails to process it along with other shapes, and has to be left till last. Overall, grammatical analysis improved the labeling result from our statistical model from 95.70% to 96.18%, proving it to be helpful in statistical model improvement. We also performed a dual-side t-test on stroke recognition rate compared to the state-of-the-art stroke recognition rate [START_REF] Wang | Combined segmentation and recognition of online handwritten diagrams with high order markov random field[END_REF], and we are having a confidence above 90% that current model is superior than [START_REF] Wang | Combined segmentation and recognition of online handwritten diagrams with high order markov random field[END_REF]. Considering that research [START_REF] Wang | Combined segmentation and recognition of online handwritten diagrams with high order markov random field[END_REF] is also conducted by us, by using MRF learned with structured SVM, they are of same origination and they are all significantly superior to flowchart recognition methods using other models.

Symbol and graph level recognition

When the stroke recognition results are available, we can process the grammatical structural analysis. This analysis enables to build both objects based on strokes, and logical relationships between recognized symbols. The novelty of our experiments is that the database now includes relationships in the ground truth. Consequently, we can evaluate structural correctness in our graph level recognition analysis. Our graphical level evaluation is done using the tools mentioned in [START_REF] Mouchère | Advancing the state of the art for handwritten math recognition: the crohme competitions, 2011-2014[END_REF].

Table 4 gives object level recognition result, specifically symbol segmentation results and symbol recognition results. Traditional recall and precision metrics compute the ratio of correctly recognized symbols to groundtruth symbols and correctly recognized symbols to all recognized symbols respectively. We can notice a higher rate for symbol segmentation than for sym- The arrow and the decision symbol are all recognized as text, while letter o is recognized as connector. This is due to the undetected decision box (as in [START_REF] Carton | Fusion of statistical and structural information for flowchart recognition[END_REF], Fig. 6). Missed boxes can not be recognized.

bol recognition because a correctly recognized symbol requires both a valid segmentation and a valid symbol label. Table 5 shows the recognition results at the global flowchart level. A diagram is considered correctly recognized only when all of its symbols are correctly segmented, correctly labeled and the structure is correctly parsed . These three requirements come in an order that a later requirement must meets a prior requirement, so in table 5 we give recognition rate under these three more and more strict requirements. It can be seen that the correctly recognized diagrams are relatively few considering all the requirements. However, we need a more detailed analysis of the causes of errors.

In Figures 8, 9 For 8(b), the only error occurs with a process box recognized as data. This implies that though grammatical analysis ensure a valid interpretation, a better flowchart recognition result can be achieved by using stronger local raw feature extractor. Compared to some researches that filtered text first as [START_REF] Bresler | Recognition system for on-line sketched diagrams[END_REF], our performance is satisfying. The goal of the additional grammatical structural analysis is to recover as much as possible these errors. However, the quality of the results will depend on the strength of the rules that are hard-coded and relies heavily on the designer experience. This is why, in some cases, the initial probabilistic model would give better results than the post-processed one. Such a situation is illustrated in Figure 10 where from the correctly labeled flowchart obtained with the max-margin MRF, cf. Figure 10(a), an incorrect interpretation is then produced applying the grammar rules, cf. Figure 10(b). To improve global recognition rate, higher order MRF should be considered and shape information incorporated grammar parser, like [START_REF] Carton | Fusion of statistical and structural information for flowchart recognition[END_REF], can be used to avoid labeling part of the node symbol into strokes.

Conclusion

In this work a mixed strategy is proposed for recognizing online handwritten flowcharts. From one hand, we develop MRF models trained using structured SVM to label the flowcharts at the stroke level. On the other hand, a syntactic approach is used to parse the results of the stroke labeling and to produce symbols with their relationships in consistence with grammar rules. In a sense, an implicit and an explicit grammar modeling are achieved with this solution. We validated our approach on a flowchart dataset that now contains a complete ground-truth, including logical order, and that is available for experiments.

Furthermore, this symbol recognition method can support additional improvements. First of all, we can balance differently the local and the global constancies. In this direction, MRF can support higher order potential functions. This could be helpful for producing better segmentation results. Secondly, a deeper integration of our MRF model and grammatical model could be studied to use a probabilistic parsing method to alleviate the dominant effect of the stroke labeling. In further research we will investigate the potential of MRF more deeply to make it more compatible to global consistency.

  Fig. 1 Two 2D handwritten languages: sketched diagrams and mathematical expressions. The diagram has much flexibility while the mathematical expression follows a rather strict grammar.

  Fig. 4 A sample sketch diagram and its corresponding MRF. Unary potential functions are represented by a solid triangle between X and Y, and pairwise potential functions are represented by a solid square between Ys. Those links indicate they are regarded as neighbors temporally or spatially.

Fig. 5

 5 Fig. 5 This graph shows raw feature pairwise relationship. Every stroke is sampled to 30 points, X 1 , X 2 , . . . , X 30 on the first stroke and Y 1 , Y 2 , . . . , Y 30 on the second stroke. Only a selected number of points are presented. The features are the displacements vectors from every sampling point from one stroke to another, as shown by dotted arrow.

  quadrilateral Q::= TERM_SEG S1 && AT(end S1) && TERM_SEG S2 && AT(end S2) && TERM_SEG S3 && AT(end S3) && TERM_SEG S4

  The predicate ProcessCond can be seen as a binary classifier of Process boxes. Then the arrow candidates are selected in an area closed to the box Pr. At the end of the arrow, another box among the previously found boxes should exist. If these conditions are satisfied the link between the arrow Arr and the next box B is saved and the recursion is called to build the remaining parts of the flowchart. If the new box B is also a Process, the same version of recursiveDiag will be used to look for the new arrow. The second part of the predicate is an example of ending predicate: the last box should be a connection box. recursiveDiag [Pr, Arr|Remaining]::= ProcessCond Pr && Pr == Process && AT(closeTo Pr) && anArrow Arr && AT(end Arr) && Box B in savedBoxes && save Arr B && recursiveDiag [B|Remaining] recursiveDiag [LastBox]::= LastBox == Connection

Fig. 6

 6 Fig. 6 This experiment shows the result of tuning of spatial distance threshold by 3-fold cross-validation. Two metrics are to decide the final choice of spatial distance threshold: inference time on per flowchart, and stroke labeling accuracy.

Fig 6

 6 Fig 6 shows the spatial distance threshold's effect on model inference time and stroke labeling accuracy.For stroke labeling accuracy before 0.03, it is increasing steady. This is due to the fact that with larger spatial distance threshold, the more connections exist for vertices on graphical models, the richness of connection provides more information of the flowchart. However, the accuracy appears to be unstable after that because expanded edges are providing a redundancy, which is

Fig. 8

 8 Fig. 8 Typical examples of flowchart recognition, with max-margin MRF stroke labeling and grammatical analysis. The strokes are colored to indicate their recognition result. The legend of Figures is shown in8(c).

Fig. 9 A

 9 Fig.9A flowchart's recognition result in two stages: 9(a)for after max-margin MRF stroke labeling and 9(b)after stroke labeling and grammatical analysis. Grammatical description would eliminate some stroke labeling errors, for example the process is confused with data symbol before grammatical analysis. Most of this type of errors are corrected after grammatical analysis step.

  (a) A correctly labeled flowchart using max-margin MRF.(b) The same flowchart recognized after grammatical analysis, which leads to error.

Fig. 10

 10 Fig.10An incorrectly recognized flowchart compared to the state before grammatical analysis. 10(a) is correctly labeled. The arrow and the decision symbol are all recognized as text, while letter o is recognized as connector. This is due to the undetected decision box (as in[START_REF] Carton | Fusion of statistical and structural information for flowchart recognition[END_REF], Fig.6). Missed boxes can not be recognized.

  and 10 we have shown four examples of labeled flowcharts: 8(a) is a correctly recognized flowchart, 8(b) is a correctly segmented but incorrectly labeled sample, and Figures 9 and 10 show incorrectly recognized flowcharts. From the examples we can have some insight of the source of the errors.

Table 1

 1 Flowchart database statistical overview. 10 writers of the Test part appear also in the Train part.

		Writers Patterns Flowcharts Strokes Symbols
	Training	30	14	248	23355	5540
	Training fold 1	11	14	76	6896	1688
	Training fold 2	11	14	83	7898	1861
	Training fold 3	8	14	89	8561	1991
	Test	15	14 other	171	15696	3791

Table 2

 2 Stroke labeling result for each class and all together before and after grammatical analysis (GA). P for precision, R for recall. (%)

			Before GA			After GA
		P	R	F1	P	R	F1
	Text	97.88 98.42 98.15 96.81 99.27 98.03
	Arrow	93.93 92.29 93.10 98.18 90.49 94.18
	Process	90.17 94.08 92.08 93.13 94.69 93.91
	Terminator 95.03 77.13 85.15 89.29 78.48 83.53
	Connection 91.87 83.70 87.60 83.22 91.85 87.32
	Data	90.00 91.56 90.77 93.28 94.59 93.93
	Decision	90.44 93.82 92.10 95.69 92.53 94.08
	All	95.71 95.70 95.67 96.19 96.18 96.14
	Accuracy		95.70			96.18

Table 3

 3 Stroke labeling result and final symbol recognition recall on the test set of flowchart dataset (%). Considering the randomness from Random Forests and GBDT, our experiment launched for 5 times, with mean and unbiased standard error recorded. This table also listed some other researches on the same dataset.

		Stroke Reco. Rate Symbol Reco. Rate
	Lemaitre et. al. [18]	91.1	72.4
	Carton et. al. [8]	92.4	75.0
	Bresler et. al. [7]	95.2	82.8
	Wu et. al. [33]	94.9	83.2
	Wang et. al. [32]	95.8	84.3
	GBDT only	80.87 ± 0.07	-
	Random Forest only	81.45 ± 0.10	-
	GBDT+RF+M3N inference	95.70 ± 0.65	-
	GBDT+RF+M3N inference+GA	96.16 ± 0.34	80.69 ± 0.85

cluster together and in a much smaller scale. Also, the biased number of training samples of different strokes are having a side-effect on recognition result: stroke classes with few samples are more likely to be misclassified to other classes.

Table 4

 4 Symbol segmentation and recognition result after grammatical analysis (%)

		Precision Recall	F1
	Text	71.06	78.93	74.79
	Arrow	72.89	76.89	74.84
	Process	84.95	89.95	87.38
	Terminator	78.21	77.83	78.02
	Connection	85.18	92.74	88.80
	Data	92.63	89.80	91.19
	Decision	82.86	82.07	82.46
	Object overall	76.13	80.85	78.42
	Segmentation	78.21	83.06	80.57

Table 5

 5 Graph level recognition on test set, considering all 171 flowchart instances

		Rate(%) Correct count
	Correct symbol segmentation	19.88	34
	Correct symbol recognition	12.87	22
	Correct symbol + structure	5.85	10

The final publication is available at Springer via http://dx.doi.org/10.1007/s10032-017-0284-8


Sébastien Lefebvre

Benoit Rannou

Stéphane Besse

Etienne Benoit

Virginie Lattard
email: virginie.lattard@vetagro-sup.fr

Origin of the gender differences of the natural resistance to antivitamin K anticoagulants in rats

Keywords: gamma-glutamyl carboxylase VKA: vitamin K antagonists Difethialone, vitamin K antagonist, susceptibility, gender differences, rat

Vitamin K antagonists (VKA) are used either in human medicine to prevent thromboembolic disorders or as rodenticides for pest control management. In rodents, female rats are described to be more tolerant to the action of vitamin K antagonists than males.

Nevertheless, the mechanism of this greatest tolerance is still unknown and this study aims to identify the origin of this greatest tolerance after VKA administration. Therefore, difethialone, one of the most powerful VKA was used in this study.

A possible difference in the pharmacokinetics of difethialone between males and females was first investigated. The determination of the pharmacokinetic parameters allowed to exclude a pharmacokinetic origin of the greatest tolerance of females to VKA. Thus, a natural resistance to difethialone of the liver VKOR activity, which is the target of VKA, was thus explored in females. The determination of Ki towards difethialone in liver microsomes allowed to also exclude this hypothesis. Therefore, equipment in vitamin K-dependent clotting factors and properties of vitamin K-dependent clotting factors were explored. Basal activity of clotting factors VII and X were found significantly higher in females of respectively 43% and 21%. Moreover, after VKA administration, half-lives of clotting factors II and X were found significantly longer in females of respectively 27% and 10% and a lag time of 4 hours before the beginning of the decay of factor VII was observed only in females after difethialone administration. The greater tolerance of female rats to VKA is thus due a stronger basal pool of vitamin K-dependent clotting factors VII and X and to a slower decline of vitamin K-dependent clotting factors II, VII and X after VKA administration.

Graphical Abstract

INTRODUCTION

In human medicine, vitamin K antagonists (VKA), derivatives of either 4-hydroxycoumarin or indane-1,3-dione, are widely prescribed in the prevention and the treatment of thromboembolic disorders. Warfarin, a derivative of 4-hydroxycoumarin, is the most used VKA worldwide and is prescribed to 2 million new patients in the USA each year. VKA are also used as rodenticides for pest control management. VKA exert their anticoagulant activity by stopping the recycling of vitamin K, which is the cofactor of oxydo-reduction reactions, including the activation of vitamin-K dependent clotting factors. The activation of vitamin-K dependent clotting factors is performed by the gamma-glutamyl carboxylase (GGCX). In the endoplasmic reticulum, GGCX converts glutamate (Glu) of vitamin K-dependent proteins in carboxylated glutamate (Gla) [START_REF] Furie | Vitamin K-dependent biosynthesis of γcarboxyglutamic acid[END_REF]. For each conversion, vitamin K hydroquinone has to be converted in vitamin K epoxide. Since the vitamin K dietary intake is not sufficient for the physiological needs [START_REF] Ferland | The Discovery of Vitamin K and Its Clinical Applications[END_REF], vitamin K epoxide needs to be recycle in vitamin K hydroquinone by a vitamin K 2,3-epoxide reductase (VKOR) activity which involves mainly a vitamin K 2,3-epoxide reductase complex subunit 1 (VKORC1) protein [START_REF] Oldenburg | Vitamin K Epoxide Reductase Complex Subunit 1 (VKORC1): The Key Protein of the Vitamin K Cycle[END_REF]. It is this enzyme which is the target of VKA.

Clotting factors II (i.e., Prothrombin), VII, IX and X are vitamin K-dependent proteins involved in the coagulation. These clotting factors need to be gamma-carboxylated to be able to chelate calcium and have a biological activity [START_REF] Bandyopadhyay | Vitamin K-Dependent γ-Glutamylcarboxylation: An Ancient Posttranslational Modification[END_REF]. The uncarboxylated vitamin K-dependent clotting factors circulate in very low level in rat blood [START_REF] Harauchi | Liver and Plasma Levels of Descarboxyprothrombin (PIVKA II) in Vitamin K Deficiency in Rats[END_REF]. Clotting factor VII is involved in the extrinsic pathway, clotting factor IX in the intrinsic pathway, prothrombin and factor X are involved in the common pathway. Consequently, active vitamin K-dependent clotting factors are necessary for coagulation. By inhibiting VKORC1 protein [START_REF] Rost | Mutations in VKORC1 cause warfarin resistance and multiple coagulation factor deficiency type 2[END_REF]Li et al, 2004), VKA block the gamma-carboxylation of vitamin K-dependent clotting factors, impairing the coagulation function.

VKA are difficult to use because of a narrow therapeutic index and a wide variability of dosage necessary to achieve stable anticoagulation. This variability is partly due to basic physiological parameters such as age, body weight, but also to co-occurring disorders, drug and food interactions. Sex-differences in the response to VKA could exist. If these differences are difficult to demonstrate in human medicine, such differences have been demonstrated in rats [START_REF] Gill | Blood-Clotting Response Test for Bromadiolone Resistance in Norway Rats[END_REF]Kerins and McNicoll, 1999). Female rats are more tolerant to VKA than males. The underlying mechanism of this resistance is still unknown.

Differences of VKOR activity could be associated with the natural resistance of females. Indeed, mutations of VKORC1 enzyme can lead to resistance to VKA [START_REF] Rost | Mutations in VKORC1 cause warfarin resistance and multiple coagulation factor deficiency type 2[END_REF]Watzka et al, 2011;Hodroge et al, 2012;[START_REF] Pelz | The Genetic Basis of Resistance to Anticoagulants in Rodents[END_REF][START_REF] Pelz | Distribution and frequency of VKORC1 sequence variants conferring resistance to anticoagulants in Mus musculus[END_REF]. If this VKORC1 mutationinduced mechanism can be excluded in the case of the natural resistance to VKA of females, differences in the expression level of genes encoding putative partner proteins of VKORC1, such as calumenin (Wallin et al, 2001), epoxide hydrolase (Guenthner et al, 1998) or glutathione transferase (Cain et al, 1998), could modify this VKOR activity. Other mechanisms could be suspected to explain the better tolerance of females to VKA, such the existence of metabolic differences between males and females [START_REF] Huber | Tissue Phylloquinone and Menaquinones in Rats Are Affected by Age and Gender[END_REF][START_REF] Markussen | Characterization of bromadiolone resistance in a danish strain of Norway rats, rattus norvegicus, by hepatic gene expression profiling of genes involved in vitamin k-dependent γ-carboxylation[END_REF][START_REF] Markussen | Differential expression of cytochrome P450 genes between bromadiolone-resistant and anticoagulant-susceptible Norway rats: a possible role for pharmacokinetics in bromadiolone resistance[END_REF]Mugford and Kedderis, 1998;[START_REF] Waxman | Interactions of hepatic cytochromes P-450 with steroid hormones. Regioselectivity and stereospecificity of steroid metabolism and hormonal regulation of rat P-450 enzyme expression[END_REF], or even a natural resistance of the coagulation cascade [START_REF] Lemini | Gender and inter-species influence on coagulation tests of rats and mice[END_REF] after VKA administration.

The aim of this study is to demonstrate first the greater tolerance of the female rats to VKA compared to males and to characterize this tolerance, and thus to identify the underlying mechanism of this greatest tolerance to VKA.

MATERIALS AND METHODS

ANIMALS

OFA-Sprague-Dawley rats were obtained from a commercial breeder (Charle Rivers, l'Arbresles, France) and acclimated for a minimal period of 5 days. The rats were housed four per cage under a constant photoperiod and ambient temperature. In order to characterize the VKOR activity, 8-weeks old OFA-Sprague-Dawley rats (4 males and 4 females) were killed by decapitation. Liver was removed quickly and microsomes were immediately prepared. In order to study the decay kinetics of the vitamin K-dependent blood clotting factors after administration of anticoagulants, 8-weeks old OFA-Sprague-Dawley rats (44 males and 44 females) have been fed with vitamin K3-deficient food (Scientific Animal Food and Engineering, Augy, France), at least 48 hours before the beginning and during the experience. To explore the basal levels of blood parameters, a first group of 8 males and 8 females were killed 48h after the beginning of the vitamin K3-deficient feeding. Blood was collected in citrate tubes (3.2%; 1:9 v/v) by intracardiac taking and liver was collected and frozen at -80°C. The other animals received by force-feeding a per os administration of 10 mg/kg of difethialone 48h after the beginning of the vitamin K3-deficient feeding, then a group of 3 males and 3 females was killed 1,2,4,8,10,13,16,20,24,32,48 and 72 hours after the difethialone administration. Blood was collected in citrate tubes (3.2%; 1:9 v/v) by intracardiac taking and liver was collected and frozen at -80°C.

MICROSOME PREPARATION

Liver microsomes were prepared by differential centrifugations as described by Moroni [START_REF] Moroni | The Flavin-Containing Monooxygenase in Rat Liver: Evidence for the Expression of a Second Form Different from FMO1[END_REF]. Briefly, liver cells were resuspended in 50 mM Phosphate Buffer (pH 7.4) containing 1.15 % (w/v) of KCl. liver cells were broken by Potter and further submitted to differential centrifugation a continuously at 4°C. The 100,000 × g pellet corresponding to the membrane fraction was resuspended by Potter homogenization in HEPES glycerol buffer (50 mM Hepes, 20% glycerol, pH 7.4). Microsomes were frozen at -80°C and used for kinetic analysis. Protein concentrations were determined by the method of Bradford [START_REF] Bradford | A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein-dye binding[END_REF] using serum albumin as a standard.

VITAMIN K EPOXIDE REDUCTASE ACTIVITY

Microsomal vitamin K epoxide reductase (VKOR) activity was assayed according to a modified protocol previously described by [START_REF] Thijssen | Warfarin resistance: Vitamin K epoxide reductase of scottish resistance genes is not irreversibly blocked by warfarin[END_REF][START_REF] Thijssen | Warfarin resistance: Vitamin K epoxide reductase of scottish resistance genes is not irreversibly blocked by warfarin[END_REF] and Thijssen and[START_REF] Thijssen | Microsomal warfarin binding and vitamin K 2,3-epoxide reductase[END_REF][START_REF] Thijssen | Microsomal warfarin binding and vitamin K 2,3-epoxide reductase[END_REF] and [START_REF] Misenheimer | Warfarin resistance in a Chicago strain of rats[END_REF][START_REF] Misenheimer | Warfarin resistance in a Chicago strain of rats[END_REF][START_REF] Misenheimer | Warfarin resistance in a Chicago strain of rats[END_REF]. Briefly, standard reactions were performed in 200 mM Hepes buffer (pH 7.4) containing 150 mM KCl, 1 mM dithiothreitol, 1 mg of total proteins. The reaction was started by the addition of vitamin K > O solution in 1% Triton X-100. After incubation at 37 °C for 30 min, the reaction was stopped by adding 4 mL of iced 1:1 isopropanol/hexane solution. After centrifugation at 5000 × g for 10 min, the hexane layer was removed and dried under nitrogen. The dry residue was immediately dissolved in 0.2 mL of methanol and reaction product was analyzed by liquid chromatography-mass spectrometry.

VITAMIN K1 MEASUREMENT

The LC-APCI/MS/MS used was a 6120 Quadrupole LC/MS with an Atmospheric Pressure Chemical Ionisation (APCI) interface and a LCMS Chemstation software from Agilent Technologies (Palo Alto, CA, USA). Chromatographic separation was performed using a XTerra MS C18 column (2.1mm × 50mm, 2.5µm, Waters, Milford, MA, USA) with a mobile phase of methanol, 0.1% acetic acid (96:4) in isochratic conditions. The column temperature was 48°C. The flow rate in the LC column was 0.4mL/min. The injection volume was 20µL.

The temperature of the autosampler tray was set to 5°C and the samples were protected from the daylight. Detection was by MS with APCI source in positive mode. Nebulizer pressure was set to 60psi, dry gas temperature to 350°C, dry gas flow to 5 L/min, and vaporizer temperature to 400°C. Capillary voltage was set to 4000V, corona needle to 10µA.

Identification criteria for vit K 1 are the retention time (tr= 3.9 min) and the selected ion 451.4. Identification criteria for vit K 1 >O are the retention time (tr=2.9 min) and the selected ion 467.0. Linearity and accuracy were tested from 25 to 2000 ng/mL (n=20). The response was linear throughout the concentration range tested with a coefficient of correlation (r 2 ) above 0.99. Accuracy was between 80 and 120% of the theoretical concentrations. In order to evaluate the inhibiting effect of warfarin on VKOR activity, inhibition parameters (Ki) were determined after addition of various concentrations of warfarin to the standard reaction. Inhibition parameters were first assessed with 4 different concentrations (0.01, 1, 10 and 30 μM) and further more precisely determined using concentrations from about 0.05 to 20 × Ki. Data were fitted by non-linear regression to the non-competitive inhibition model using Sigmaplot 9.0™ software.

DETERMINATION OF DIFETHIALONE CONCENTRATION IN LIVER

Tissue (1g of tissue) was extracted with acetone by using an Ultra Turrax tissue disperser from IKA Labortechnick ® (VWR International, Strasbourg, France). Extract was centrifuged at 3000 × g for 10 min. Supernatant was thus evaporated at 60°C under a gentle nitrogen flow. Dry extract was resuspended in acetonitrile/hexane (v/v 50/50). The hexane layer was eliminated and the rest was dried at 60°C under gentle nitrogen flow. The final dry extract was dissolved in methanol and difenacoum concentration was analysed by HPLC on a reverse phase C-18 column (4.6×150 mm, 5 μm; Waters, Milford, MA, U.S.A.) at a detection wavelength of 260 nM. The C-18 column was heated 30°C. A gradient elution system was used with a flow rate of 1 mL/min: from 60% acetonitrile/40% water (acidified with 0.2 % H3PO4) to 75 % acetonitrile/25% water at 10 min. The detection limit and the quantification limit were 50 ng/g and 130 ng/g. The specificity of the analytical method was determined by the extraction of three different blank samples of each organs collected from adults rats. The method appeared selective for all the components. The noise level were estimated for each organs and the mean value plus three standard deviations or ten standard deviations were used respectively to calculate the limit of detection (LOD) and the limit of quantification (LOQ). Spiked samples with decreasing concentrations were used to determine those limits chromatographically. The linearity and accuracy were determined on liver and plasma spiked samples. Three series of seven spiked samples were prepared (each one on different day) then extracted and analyzed. The linear regression equations of spiked samples were compared to standards calibration curves (r 2 > 0,99).

QUANTITATIVE REAL TIME-PCR

Total RNAs were extracted from liver first with the Trizol reagent (Invitrogen, Cergy Pontoise, France) then by using SV Total RNA Isolation System (Promega, Charbonnieres, France).

The RNA concentration and purity were analyzed using a UV-160A spectrophotometer (Shimadzu, Roucaire, France), measuring spectral absorption at 260 and 280 nm. cDNA templates were synthesized from 100 ng total RNAs in a final volume of 20 µL containing 500 pmol of oligo(dT) 18 and 200 units of Moloney murine leukemia virus Reverse Transcriptase (Invitrogen, Cergy Pontoise, France) according to the manufacturer's protocol.

Quantitative real time-PCR reactions were performed with the MX3000P qPCR Machine (Stratagene, Amsterdam, The Netherlands) using primers for Ggcx, Nqo1, Vkorc1, Vkorc1l1, Calu (Calumenin), F2 (prothrombin), F7 (factor VII), F9 (factor IX) and F10 (factor X). Gapdh was used as housekeeping gene. The housekeeping gene was amplified under the same conditions used for the amplification of the target genes. Briefly, in a final volume of 20 µL, 5 ng of cDNA were added to an optimal amplification reaction mixture containing 5X HOT BIOAmp Evagreen ® qPCRMix (Biofidal, Vaux-en-Velin, France) and 200 nM of each primer. Thermal cycling was the following: activation of the HOT BIOAmp® DNA Polymerase at 95°C for 5 min and 45 cycles of amplification (95°C for 20s, 60°C for 60s and 72°C for 30s). To determine the specificity of amplification, analysis of product melting was conducted after the 45 cycles of amplification: a melting curve was obtained by increasing the temperature at a rate of 0.01ºC per second from 60ºC to 95ºC. Expression was evaluated in duplicate. The point at which the PCR product is first detected above a fixed threshold, the thermal cycle threshold (C t ), was determined for each sample, and the average C t of duplicate sample was calculated. To determine the quantity of the target gene-specific transcripts present in different tissues relative to the control, their respective Ct values were normalized by subtracting the Ct value obtained from the Gapdh control (rCt = Ct target -Ct control) and the relative concentration was determined with the following formula: 2 -rCt .

DETERMINATION OF CLOTTING FACTOR CONCENTRATIONS

Vitamin K-dependent clotting factors activities (II, VII, IX, X) were measured on citrated plasma using a chromogenic method on Konelab 30i (Thermoscientific) with Hyphen Biomed reagents.

More precisely, factor II was activated by incubation of citrate plasma with Echis Carinatus venom (0.25 mg/mL) in Tris-buffer (0,1mM Tris Hcl, pH 8.3 at 25°C, 0.2% BSA) at 37°C for 10 min. Thus, 50 µg of thrombin chromogenic substrate was added and absorbance was monitored at 405 nm for 1 min.

Factor VII activity was assayed by incubation of citrate plasma with calcium and tissue factor in excess to allow formation of tenase complexes and addition of a saturating concentration of human factor X activated in factor Xa proportionally to the quantity of tenase complexes formed. Thus, activity of factor Xa was monitored at 405 nm for 2 min after the addition of a specific chromogenic substrate generating para-nitroaniline in the presence of factor Xa.

Factor IX activity was assayed by an initial incubation of thrombin, calcium, phospholipids and Factor XIa with citrate plasma. The addition of a second reagent allowed to add factor VIII:C and factor X in the mixture. Thus, 50 µg of thrombin chromogenic substrate was added and absorbance was monitored at 405 nm for 1 min.

Factor X was activated by the addition of Russel's viper venom. Thus, 50 µg of thrombin chromogenic substrate was added and absorbance was monitored at 405 nm for 2 min.

2.9 STATISTICAL ANALYSIS Statistical analysis were performed with R v. 3.1.2. Results were expressed as mean values ±SD or fitted value and confidence interval. Concerning the biochemical part, as the values are in small number, Wilcoxon-Mann-Whitney tests were used to assess the difference between males and females. To compare results between males and females for the basal levels, Student tests were performed as values are normally distributed. For the decrease of each clotting factor after the administration of diféthialone, data were linearized with a logarithmic function. Males and females regression curves were compared on the slope parameters with a Fisher test on the variance. The null hypothesis is that the male and female curves have the same slope.

RESULTS

MRNA EXPRESSION OF KEY ENZYMES INVOLVED IN THE VITAMIN K CYCLE IN LIVER

The presence of mRNA for Ggcx, Vkorc1 or Vkorc1l1 was assessed by real time PCR in liver of 8 weeks-old male and female OFA-sprague Dawley rats. Results are presented in Figure 1. mRNA expression levels were presented relatively to the corresponding male mean mRNA expression level, which was set at 100%. Results are presented in percentage of expression compared to the expression level obtained in male. Expression levels of Ggcx and Vorc1l1 mRNA were similar between males and females. On the contrary, a significant difference between males and females was found concerning the expression of Vkorc1 mRNA coding gene. Vkorc1 mRNA was found to be 80% more expressed in female liver compared to males (Figure 1).

VKOR ACTIVITY

To compare the ability to reduce vitamin K epoxide in vitamin K quinone between male and female rats, liver microsomes from 4 males and 4 females OFA-Spradue-Dawley rats were prepared. Then the catalytic properties of the VKOR activity measured in these microsomes were determined. Km and Vmax results are presented in Table 1. A statistic difference was found between males and females only concerning the Vmax value. The specific activity of females was 2.4 fold higher than males.

BASAL LEVELS IN VITAMIN K-DEPENDENT CLOTTING FACTORS ACTIVITIES

The concentrations of vitamin K-dependent clotting factors (i.e., prothrombin, factor VII, factor IX and factor X) were measured in males and females 48 h after the beginning of the vitamin K3-deficient food. Concentrations were determined relatively for each factors to the corresponding male mean concentration factor (Figure 2A, Table 2) set at 100%. A significant difference was found between males and females for factor VII (P<0.001) and factor X (P=0.006) with a clotting factor concentration in females higher than males of respectively 43 and 21 percent. But considering the factor IX and the prothrombin no significant difference was found.

In addition, a study of the hepatic expression of vitamin K-dependent clotting factor genes: prothrombin, factor VII, factor IX and factor X was performed (Figure 2B). mRNA expression levels were presented relatively to the corresponding male mean mRNA expression level, which was set at 100%. Only Factor VII expression was significantly different between males and females (P<0.001), females' factor VII expression was 125 percent higher than males' factor VII expression.

EVOLUTION OF CLOTTING FACTORS AFTER DIFETHIALONE PER OS ADMINISTRATION

In order to characterize the decay kinetics of vitamin K-dependent clotting factors, an elevated concentration of difethialone (10 mg/kg) was administered per os to 36 male and 36 female rats previously fed with vitamin K3-deficient food for 48h. For each rat prothrombin time was measured and vitamin K-dependent clotting factors activities (prothrombin, factor VII, factor IX and factor X) were measured in citrate plasma. For 3 males, the blood collection was impossible because of their premature death; the first one, ten hours after the difethialone administration and the others seventy-two hours after the administration.

Necropsy has showed hemorrhagic lung and abdomen in these rats.

The evolution of prothrombin time after the administration of difethialone for male and female rats is presented in Figure . After the linearization of data (Figure B), a two steps evolution of prothrombin time was pinpointed. A lag time was present in both male and female prothrombin time evolutions. However, this lag time has occurred during 2 first hours in males and 8 first hours in females, lag time slopes were not different from 0 with respectively a p-value of 0.16 and 0.46. Then both prothrombin time evolutions increased with a slope of 0.04 h -1 for male rats and 0.05 h -1 for female rats. The two increasing slopes were significantly different (P<0.001).

The plasma activities of vitamin K-dependent clotting factors are represented in function of time after difethialone administration in Figure 4. The activity values are represented relatively to the male basal level set at 100%. To assess the evolution of clotting factors, data were linearized with a natural logarithmic function (Figure X2) allowing to determine the slope and the half-life (Table 3). A significant difference was observed between male rats and female rats for the prothrombin and the factor X slope values. Consequently, the half-lives of these two factors were different between males and females. Concerning female factor VII, only values from 4 hours were including in the linear regression. Indeed, during these 4 first hours, female factor VII activities did not decay. The slope of the female factor VII plateau was not significantly different from 0 (p-value = 0.409). One,2,4,8,10,13,16,20,24,32,48 and 72 hours after the per os difethialone administration, difethialone concentration in plasma liver was determined. The concentration of difethialone in plasma (data not shown) and liver (Figure 5) increased rapidly after an oral administration in males and females, reached a peak about 8-12 h after the administration, and then decreased slowly an a time-dependent manner. The maximal concentration in plasma and liver was significantly reached earlier in females (T max =7.9 h) than males (T max = 11.7 h). Pharmacokinetic analyses (Table 3) revealed that C max and AUC 0→24h or AUC 0→72h were significantly higher in females than males.

EVOLUTION OF THE DIFETHIALONE CONCENTRATION IN LIVER

DISCUSSION

The resistance of female rats to the administration of anticoagulants is a phenomenon well recognized [START_REF] Gill | Blood-Clotting Response Test for Bromadiolone Resistance in Norway Rats[END_REF][START_REF] Kohn | Genomic assignment of the warfarin resistance locus, Rw, in the rat[END_REF]. In practice, discriminating doses of anticoagulants, called ED50 (i.e., effective dose 50), were determined in rats to characterize the susceptibility of rats to anticoagulants. ED50 corresponds to the dose leading to 50% of animals tested with a 5-fold increase of the International Normalized Ratio 24 hours after the administration of anticoagulants. Systematically for all the anticoagulant molecules used as rodenticides, the ED50, determined by the Rodenticide Resistance Action Committee, are higher for female rats than males. For example, as recommended by the technical monograph of 2003, ED50 for difethialone is 0.4 mg.kg -1 for male rats; it is 0.5 mg.kg -1 for females. Contrary to rats, in humans, the differences in responses after antivitamin K anticoagulants between men and women are difficult to appreciate. In healthy individuals, available studies are logically always performed with small doses of antivitamin K anticoagulants, while in diseased individuals, used doses and molecules of VKA are often different and moreover, the first evaluations of the coagulation are generally made 3 days after the initiation of the treatment.

Since the pinpointing of the female rats tolerance to VKA, many assumptions on its origin have been issued. Is the pharmacokinetics of VKA different between males and females? Is the recycling of vitamin K and more precisely the VKORC1 enzyme more resistant to VKA in females than males? Is the half-life of vitamin K-dependent clotting factors longer in females than males? Is the vitamin K storage higher in females than males?

To answer these questions, the greater tolerance of the female rats to VKA was first characterized after administration of 10 mg.kg -1 of difethialone by following the timedependent evolution of the prothrombin time. Difethialone was chosen in this study because it is one of the most powerful rodenticides. No resistance to this molecule has been described until now (Hodroge et al, 2011). An excessive dose of difethialone, corresponding approximately to 20-fold the DL50 (Petterino and Paolo, 2001), was administered to male and female rats. In these conditions, we can assumed that VKORC1 is totally inhibited in males, but also, in females since the inhibition constants of the VKOR activity towards VKA are not different between sexes. Moreover, we can also assume that the complete inhibition of the VKOR activity occurs at the same time, in the liver of male and female rats. Indeed, after per os administration, difethialone is totally and rapidly absorbed. The concentration peak in liver occurring sooner in female rats, a faster absorption of difethialone in females can be supposed. Thus, a complete inhibition of VKORC1 in the liver could even occur earlier in females. Moreover, the liver concentration of difethialone was systematically higher in females than males, as described for warfarin [START_REF] Zhu | Gender differences in pharmacokinetics of oral warfarin in rats[END_REF] suggesting a lower metabolism or elimination of difethialone in females than males. Therefore, complete inhibition of VKORC1 is assumed to be at least equivalent between males and females during the first 24 hours following the administration of difethialone. This complete inhibition of VKORC1 results in a significant increase of prothrombin time 24 hours after the administration of difethialone in males, but also in females. Nevertheless, a lag of at least eight hours in the increase of the prothrombin time was pinpointed in females compared to males (Figure ). The lag time was sufficiently important to keep the females' prothrombin times significantly lower than males' for 24 hours, even though the increase of the prothrombin time was significantly higher in females than in males after the lag.

Moreover, only males were found dead during the study and the necropsy confirmed the hypocoagulability as the origin of the death. These results argue for a highest tolerance of females compared to rats at least during the first 24 hours and this highest tolerance is not due to a pharmacokinetically-or pharmacodynamically-mediated difference in the inhibition of VKORC1 enzyme.

To go further in the understanding of the origin of females' tolerance, vitamin K-dependent clotting factors activities were measured. Even before the administration of VKA, significant differences were found between males and females. Basal clotting factor VII and X activities were found to be significantly higher in females than males. These results are in agreement with previous results obtained in Wistar rats where factors II and X activities were also observed to be higher in females than males [START_REF] Kerins | Comparison of the half-lives and regeneration rates of blood clotting factors II, VII, and X in anticoagulant-resistant and susceptible Norway rats (Rattus norvegicus Berk.)[END_REF]. In humans, all vitamin K-dependent clotting factors activities were also reported to be higher in women [START_REF] Favaloro | Crosslaboratory audit of normal reference ranges and assessment of ABO blood group, gender and age on detected levels of plasma coagulation factors[END_REF]. In OFA-Sprague Dawley rats, these highest activities in females' livers do not seem to be due to higher mRNA syntheses in liver, except eventually for factor VII. Indeed, only, mRNA encoding factor VII were found to be 2.3-fold more expressed in female rats' livers than males, The expression levels of the other mRNA encoding factors II, IX and X were similar between males and females. The highest factor VII and X plasma activities observed in females might be explained by the highest rate of the VKOR activity measured in females livers (i.e., 2.4 fold) compared to males. These highest basal activity of active vitamin K-dependent clotting factors in females are certainly involved in the explaining of the sex-linked clotting time differences previously observed [START_REF] Lemini | Gender and inter-species influence on coagulation tests of rats and mice[END_REF].

Moreover, this higher initial pool of active vitamin K-dependent clotting factors VII and X might be a part of the explanation of the highest tolerance of the female rats. Nevertheless, this initial difference is strengthened by longer decay kinetics of vitamin K-dependent clotting factors II, VII and X in females after administration of difethialone. Indeed, half-lives of factors II and X are significantly higher in female rats than males, with half-lives longer of respectively 2.7 and 0.5 hours. For factor VII, no difference of half-lives was observed between males and females. Nevertheless, this absence of difference is due to the calculation method. Since factor VII activities were not modified between the first 4 hours following difethialone administration in females, the calculation of half-life in female was performed in this study considering only the results obtained after the first 4-hours period. Therefore, when the lag time is included in the calculation, loss of 50% of active factor VII activity is reached in 5.8 hours after difethialone administration in females while in males the same loss is reached in only 2.8 hours. Such lag times were previously reported in rats for factors II, VII and X by [START_REF] Kerins | Comparison of the half-lives and regeneration rates of blood clotting factors II, VII, and X in anticoagulant-resistant and susceptible Norway rats (Rattus norvegicus Berk.)[END_REF]. Nevertheless, lag times were observed in females, but also in males. In our study, the use a vitamin K3-deficient food for a preliminary period of 48 hours before difethialone administration led to an absence of lag times in males for all vitamin K-dependent clotting factors and an absence of lag time in females for factor II and X. The lag time observed in females before the degradation of the factor VII is observed while the VKORC1 enzyme is totally inhibited. The maintained factor VII clotting factor activity might be due to a maintained GGCX activity which is strictly dependent on the bioavailability of vitamin K hydroquinone. This suggests the presence of a storage of vitamin K in female livers only allowing the preservation of the gammacarboxylation function during the first hours following the VKA-induced inhibition of the vitamin K recycling. The recycling of vitamin K in males should allow to produce just the vitamin K necessary for the physiological needs. In females, this recycling might produce more vitamin K than the physiological. Previous study has already showed that the liver concentration of vitamin K is more important in female rats than in males [START_REF] Huber | Tissue Phylloquinone and Menaquinones in Rats Are Affected by Age and Gender[END_REF]. This stock of vitamin K in females seems to be used after the inhibition of the VKOR activity to preferentially maintain the gamma-carboxylation of factor VII, which plays a crucial role in the initiation of the coagulation. The binding of the gamma-carboxylase to its protein substrates is mediated by a propeptide sequence present in all vitamin K-dependent proteins. Depending of the sequence of this propeptide, its apparent affinities for the carboxylase vary over a 100-fold range. Thus, it was shown that human factor VII and factor X propeptides have higher affinities for the gamma-carboxylase than other propeptides [START_REF] Chu | A mutation in the propeptide of Factor IX leads to warfarin sensitivity by a novel mechanism[END_REF][START_REF] Stanley | Amino Acids Responsible for Reduced Affinities of Vitamin K-Dependent Propeptides for the Carboxylase[END_REF]. In rats, no information is available. Our results suggest in rats a higher affinity of the gamma-carboxylase for the propeptide of factor VII compared to those of factor II and X. As the affinity of the gamma-carboxylase for the propeptide is determined by the propeptide sequence, it would be assumed that the gamma-carboxylase affinity is similar between male rats and females. Consequently, the absence of the plateau before the decay kinetics of factor VII and the shortest half-lives of factors II and X in males are certainly due, after the inhibition of the vitamin K cycle, to the absence of the cofactor of the gamma-carboxylase, the vitamin K hydroquinone, while in females the stock of vitamin K allowed to maintain the gamma-carboxylation of factor VII and in a lesser extent factors II and X during few hours after difethialone administration.

CONCLUSION

The tolerance of female rats to vitamin K antagonist administration is due to both the basal level of their vitamin K-dependent clotting factor activities and the half-lives of these clotting factors. Factor II, VII and X activities are higher in females than male rats. Moreover, plasmatic half-lives of prothrombin and factor X are higher in female too. Concerning factor VII in female rats, a lag time before its decay has been observed only in females and seems to be crucial in the tolerance of females to VKA. Values were compared between males (set at 100%) and females and presented as the mean ±SD. * denotes a significant between males and females at α=0.01. ** denotes a significant between males and females at α=0.001.

2. 5

 5 KINETICSKinetic parameters (Km and Vmax) were obtained from at least two separate experiments after the addition of increasing amounts of vitamin K > O (0.003-0.2 mM) to the standard reaction. The estimation of the kinetic parameters was achieved by the incubation of at least 8 different concentrations of vitamin K > O. Incubations were performed in duplicate. Data were fitted by nonlinear regression to the Michaelis-Menten model using R software.

Figure Captions

  Figure Captions

Figure 1 :Figure 2 :

 12 Figure 1: Hepatic expression levels of genes coding for three enzyme implicated in

Figure 3 :

 3 Figure 3 : Evolution of the prothrombin time after per os administration of 10 mg.kg -1

Figure 4 :

 4 Figure 4 : Evolution of activity of the four vitamin K dependent clotting factors and

Figure 5 :

 5 Figure 5 : Evolution of difethialone concentration in liver after difethialone per os

Table 3 :

 3 Hepatic pharmacokinetic summary of difethialone treatment in male and

		AUC 0→24h	AUC 0→72h	C max	T max
		(µg/g * h)	(µg/g * h)	(µg/g)	(h)
	Male	753 ± 123 *	1921 ± 291	36.3 ± 6.0	11.7 ± 0.06
	Female	1376 ± 209 *	3578 ± 560	64.5 ± 9.7	7.9 ± 0.3
	p-value	<0.05	<0.05	<0.05	<0.001

ACKNOWLEDGEMENTS

This work was supported by grants ISI n°I1301001W "NEORAMUS" from Bpi France.

Abbreviations

Gla: carboxylated glutamate Glu: glutamate