Christophe Guitton
email: <christophe.guitton@chu-nantes.fr

Nathalie Gérard

Véronique Sébille

Cédric Bretonnière

Olivier Zambon

Daniel Villers

Béatrice Charreau

C Dric Bretonni

Bé Atrice Charreau

Early rise in circulating endothelial protein C receptor correlates with

Keywords: Adult, Aged, Antigens, CD, blood, Female, France, Humans, Intensive Care Units, Male, Middle Aged, Outcome Assessment (Health Care), Receptors, Cell Surface, blood, Sepsis, physiopathology, Severity of Illness Index, Vasculitis, physiopathology

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

Author Keywords soluble EPCR ; severe sepsis ; gender ; infection ; survival analysis Severe sepsis is associated with systemic inflammation and exacerbated procoagulant state mediated by the Tissue factor (TF) pathway

. The protein C (PC) anticoagulant pathway is a major system that prevents blood coagulation, its impairment influence vital [1 -2 ] outcome in sepsis. This pathway involves PC and protein S, and two endothelial receptors, thrombomodulin (TM) and the endothelial cell protein C receptor (EPCR). Conversion of PC to activated PC (APC) is initiated by thrombin bound to TM on endothelial cell (EC) surfaces. Binding to EPCR increases the rate of PC activation by thrombin-TM complexes . APC has anticoagulant effects but also [START_REF] Fukudome | Identification, cloning, and regulation of a novel endothelial cell protein C/activated protein C receptor[END_REF] exhibits anti-inflammatory , and antiapoptotic effects . EPCR also serves as a cellular binding site for Factor VII/VIIa . EPCR (CD201) is a 46-kilodalton type I transmembrane protein, which is expressed mainly on the luminal surface of EC from large vessels and which is homologous to major histocompatibility complex class I/CD1 family proteins . Disruption of the gene in [START_REF] Laszik | Human protein C receptor is present primarily on endothelium of large blood vessels: implications for the control of the protein C pathway[END_REF] EPCR mice causes placental thrombosis and embryonic lethality confirming the key role for EPCR in controlling coagulation . [START_REF] Gu | Disruption of the endothelial cell protein C receptor gene in mice causes placental thrombosis and early embryonic lethality[END_REF] A soluble form of EPCR (sEPCR) has been described in plasma . sEPCR can be generated by ectodomain shedding mediated [12 ] [13 ] by TACE/ADAM17 or/and, by alternative mRNA splicing in haplotype-A3 carrying cells . sEPCR binds both PC and APC with [START_REF] Qu | Regulated endothelial protein C receptor shedding is mediated by tumor necrosis factor-alpha converting enzyme/ADAM17[END_REF] - [START_REF] Saposnik | Alternative mRNA is favored by the A3 haplotype of the EPCR gene PROCR and generates a novel soluble form of EPCR in plasma[END_REF] an affinity similar to that of membrane EPCR(mEPCR) . Binding of APC to sEPCR interferes with binding of APC to phospholipids [START_REF] Liaw | Mechanisms by which soluble endothelial cell protein C receptor modulates protein C and activated protein C function[END_REF] and inactivation of factor Va. Furthermore, binding of PC to sEPCR does not enhance APC generation, suggesting a procoagulant effect of sEPCR , .

[9 17 ]
EPCR levels vary in a wide variety of pathophysiological conditions, and the consequences depend partly on whether it is the membrane-associated or soluble form that is affected , . While the role of membrane-associated EPCR is clearly antithrombotic [12 18 -19 ] and anti-inflammatory in physiological circumstances, the function of the circulating sEPCR remains unclear.

Regulation of circulating sEPCR upon inflammatory disease has not been determined. Thus, whether sEPCR levels may have a predictive value of sepsis outcome is still unknown. In the present study, we investigated the kinetic of soluble EPCR levels in a cohort of 40 patients with severe sepsis upon the 5 first days in our Intensive Care Unit (ICU). The first objective was to compare sEPCR levels in septic patients at admission to healthy volunteers or to patients with active inflammatory disease. The second aim was to investigate the time course of circulating sEPCR at the onset of severe sepsis in correlation with clinical parameters and outcome at D28.

Patients, Materials and Methods

Study population

We recruited consecutive patients with severe sepsis in a 20 beds Medical ICU (Nantes University Hospital, France). Patients were included using the inclusion criteria according to the ACCP consensus definition for severe sepsis and as described in the

[20 ]

Electronic .

Supplementary Material 1 (ESM1)

The exclusion criteria were age younger than 18 years, patients without informed consent, patients not expected to survive more than 48h (moribund) or not expected to survive more than 28 days given preexisting conditions.

We collected baseline characteristics of the patients, including demographic information, severity score at admission, simplified acute physiology score (SAPS), Sepsis-related Organ Failure Assessment (SOFA) at admission and for 4 days, comorbidities, site and type of infection, and hematologic tests. Patients were followed for 28 days and/or until ICU discharge.

Blood collection

Blood was collected from patients within 24h of meeting the definition of severe sepsis (within the first 24 hours after the first organ dysfunction occurred) and daily in the 4 consecutive following days. For that purpose, blood samples were collected in the entrance in ICU (Day 1) and each morning using daily routine blood puncture (Day 2 to Day 5). After centrifugation, samples were immediately frozen as aliquots ( 80 C).

-°This study also included blood samples from patients with active systemic vasculitis (n 25) including Wegener granulomatosis (WG)

= or microscopic polyangeitis (MPA) that we previously described and blood samples from healthy adult blood donors (n 40) provided ç

Elisa assays for soluble EPCR

Quantification of sEPCR in plasma samples was carried out using ELISA kits (Asserachrom, Stago-Diagnostica, France).

Research ethics

The study was approved by medical research committee (Nantes University Hospital, France). Informed consent was obtained from the patient/substitute decision-maker before inclusion in this study. All data were anonymous.

Statistical Analysis

The means and SD or the median IQR , in case of non-normality of the distributions, are reported for continuous variables.

The

[ ]
number of patients in each category and the corresponding percentages are given for categorical variables. Non parametric ANOVA was used for the comparison of sEPCR levels at admission between groups.

Multivariate analyses were performed to study the evolution of sEPCR levels over time. To account for the correlation between measurements from the same individual, repeated measures ANOVA using linear mixed models allowing for random effects with restricted maximum-likelihood estimation were used to examine changes in sEPCR levels over time and potential interactions when appropriate ( time effect ), as well as the effect of covariates of interest ( group effect ). Several covariance structures among the repeated

" " " "
measurements (autoregressive, unstructured etc.) were compared using Akaike s Information Criterion and Schwarz Bayesian Criterion.

'

Random intercept models with autoregressive covariance structures often provided the best fit to the data. Residual analysis was used to evaluate the validity of the models assumptions including normality and homoscedasticity. An iterative stepwise selection procedure was used to select the variables that were significantly associated with the time course of sEPCR levels (variable candidates for the model were those associated with sEPCR evolution in univariate analyses with p<0.20 criterion and subsequently selected in the model using p<0.05 criterion). All measurements were transformed by calculating the natural logarithm and all analyses were adjusted on sEPCR levels at day1 in repeated measures models.

Multivariate analyses were subsequently performed using exact logistic regression and a similar strategy was used with an iterative stepwise selection procedure to select the variables that were significantly associated with day-28 survival, as assessed by the likelihood ratio test. The area under the receiver operating characteristic (ROC) curve was estimated for sEPCR levels at day 2.

Statistical analyses were performed with SAS 9.1 statistical software (SAS Institute, Cary, NC, USA). P-values <0.05 were considered to be statistically significant.

Results

Study population

Between

Soluble EPCR levels in patients with severe sepsis at admission (Day1): comparison with patients with inflammatory disease and healthy volunteers

Soluble EPCR was quantified concomitantly in all samples (n 182 for sepsis and n 65 for healthy controls and vasculitis) using a = = dedicated Elisa assay. When sEPCR levels were compared at the time of admission (D1), no significant difference ( ) was found Figure 1 between patients with severe sepsis (Med IQR :115 145 ; Mean SD: 174 117 ng/mL) compared with healthy control subjects (156 65 ;

[ ] [ ] ± ± [ ]
170 63 ng/mL; p 0.37) and with patients with active systemic vasculitis (WG and MPA)(159 94 ; 157 60 ng/mL). As compare to the

± = [ ] ±
healthy controls, sEPCR values in septic patients exhibit larger variability, especially above the median value (115 ng/mL). For further analysis, septic patients will be divided in 2 groups (High sEPCR> 115 ng/mL and Low sEPCR 115 ng/mL) according to their basal ≤ sEPCR levels at Day1.

Time course of soluble EPCR levels at the onset of severe sepsis

A retrospective and concomitant determination of circulating sEPCR was performed on blood samples collected from 40 patients with severe sepsis during the 5 first days in ICU. Quantification of circulating sEPCR in the overall population of patients ( ) mainly Figure 2a showed only slight variations in the sEPCR levels at onset of sepsis. No significant change was observed from D1 to D4 while a significant decrease was found at D5 (p< 0.05 versus D1, D2 and D3). Overall changes in sEPCR levels from D1 to D4 were low and remained below 10 of basal (D1) sEPCR rate. Similarly, although significant, decrease at D5 was moderate and around 15 of basal % % rate.

This pattern of release was consistently observed whatever the level of sEPCR in patients at D1 ( ); higher levels (H group) ESM2a were maintained during the 5-days follow-up (group effect, p<0.01).

Next, uni-and multivariate statistical analysis were performed to identify factors influencing sEPCR kinetics. These parameters were selected according to their relevance to demographics and severe sepsis (early disease severity scores, disease evolution and infection).

Variables analyzed include gender, age, outcome at D28, SAPS II, SOFA D1, SOFA D2, Gram staining, site of infection (pneumoniae), septicemia. First that time course of sEPCR release was clearly affected in septic patients according to patient survival at D28 ( ). Figure 2b Univariate analysis showed a significant difference in sEPCR levels (Group effect GE , p 0.029), and in kinetics (Time effect TE p " " = " " = 0.016) between the 2 groups. These results were confirmed in multivariate analysis (GE, p 0.003 and TE, p 0.005). At Day 2 : patients p<0.05). Nevertheless, no significant impact of gender on sEPCR profiles was found in our cohort using our statistical analysis model (

) and similar time courses were observed for males and females. Similarly, age had also no influence on sEPCR profile. ESM2b

Considering variables related to severity of sepsis, SAPS II and Mc Cabe scores had no impact. Interestingly, a weak effect of SOFA score at D1 and D2 was found on sEPCR levels (GE respectively p 0.045 and 0.034) but with no significant impact on the kinetic from D1 = to D5. To further investigate these results, correlations were examined considering individual time points. Interestingly, a slight correlation was only found between sEPCR D2 and SOFA D2 ( 0.293, p<0.05).

ρ= Finally considering parameters related to infection, we found that the presence of a positive blood culture (not shown) or pneumonia as septic localisation (

) had no effect on sEPCR profiles. In contrast, a significant impact of gram negative bacterial infection was ESM2c observed (

). Univariate analysis showed higher D1-D5 plasma levels (GE p 0.034) without clear effect on kinetic (TE p 0.376)

ESM2d = =
while multivariate analysis confirmed the influence of gram negative on both, group level and kinetic (GE p 0.045 and TE p 0.005).

= =

Overall, our findings show only slight variations in the course of sEPCR at the onset of sepsis. It appears that most of parameters affecting basal sEPCR rate have no incidence on the kinetic profile of sEPCR upon sepsis. However, we demonstrated that both level and kinetic of sEPCR are clearly influenced by Gram negative infection and, importantly, by D28 mortality: an early significant increase in sEPCR rate at D2 being associated with a poor outcome.

Consequently, to sustain this conclusion, uni-and multi-variate analyses were performed for eleven parameters (including sEPCR at D2) relevant to D28 mortality in septic patients. These parameters include sEPCR D2, sEPCR D1 H/L, SAPS II, Gender, SOFA score at D1 and D2, Age, McCabe Score, Sepsis localisation (Pneumoniae), septicemia and Gram negative infection. Major findings are reported in . Plasma concentration of sEPCR at D2 was the only variable found significantly associated with D28 mortality in multivariate Table 2 analysis (p 0.0095). Our data indicate that an increase in sEPCR at D2 of 100 ng/mL corresponds to an Odd Ratio of 2.44 1.22 5.95 .

= [ - ]
We undertook a specific analysis to further investigate the accuracy of sEPCR value at D2 to predict D28 mortality in our cohort.

Sensitivity and specificity are presented in the ROC curve ( ). The accuracy estimated by area under the ROC curve seemed ESM3 satisfactory (AUC 0.819; IC 0.658 0.971 ). The moderate size of the samples (dead 9, alive 31) is, however, a limit for further

= [ - ] = =
extrapolation.

Discussion

During sepsis, blood coagulation is activated by TF expressed on the endothelium and monocytes/macrophages in response to cytokines . Inflammatory processes can shift the hemostatic balance toward thrombus formation not only by stimulating TF-dependent [START_REF] Esmon | Coagulation and inflammation[END_REF] coagulation but also by inhibiting anticoagulant and fibrinolytic pathways . EPCR is a key factor controlling coagulation through the [START_REF] Aird | The role of the endothelium in severe sepsis and multiple organ dysfunction syndrome[END_REF] binding of both PC and APC. Inhibition of EPCR binding of PC or APC was also found to exacerbate the septic response .

[ 24 -25 ] However, clinical and functional impact of its soluble counterpart remains to be established. Here, we examined for the first time the kinetic of plasma sEPCR in a cohort of patients at the onset of severe sepsis.

First, when comparing baseline levels of sEPCR in septic patients at admission we found no significant difference with healthy controls and patients with active vasculitis, although variation among the septic patients was important. In previous studies, sEPCR levels in septic patients were found significantly higher , , similar or even lower , than in healthy volunteers. These discrepancies

[12 26 ] [27 ] [28 ]
may reflect the distribution of the A3 haplotype (15 20 ) among the cohorts since this haplotype is associated with higher baseline levels -% of sEPCR .

[18 ]

Moreover, we observed here that gender ratio may be another key factor affecting D1 sEPCR in septic patients. A similar difference was found in healthy donors. These results confirm our previous data indicating that gender was a critical parameter determining basal level of sEPCR . Although clinical impact of gender on sepsis outcome is still controversial , whether males and females [START_REF] Guitton | Circulating EPCR: endothelial regulation and cumulative impact of gender and A3 haplotype[END_REF] [ 30 -32 ] differently respond to infection is important for both clinical care and the design of clinical trials. However, probably due to the small size of this cohort and to relative variability of basal sEPCR levels, this study was unable to demonstrate an impact of gender on the sEPCR time course. Since no DNA samples were available for genetic analysis, the respective impact of EPCR haplotype and gender was not investigated.

Next, profiling sEPCR during the 5 first days of the disease showed no change in the level of sEPCR from D1 to D4 before a significant decrease at D5. Overall variations in sEPCR concentrations remain below 15 of baseline. Interestingly, this kinetic was found % consistently in septic patients regardless of basal level and gender. Another interesting observation is that, overall, sepsis only induces a moderate variation of sEPCR plasma level as suggested by initial reports , . Together these data suggest that level of sEPCR is [12 27 ] tightly controlled even upon inflammation . This hypothesis is comforted by our results obtained using cultured vascular EC. in vivo Indeed, we found that inflammation downregulates the cell surface expression of EPCR without affecting the production rate and in vitro kinetic of its soluble form (Data not shown and ).

All available data concerning simple coagulation disorders were noted (platelet count, Prothrombin time, activated partial thromboplastin time (aPTT) ratio patient/witness, and fibrinogen). The impact of these parameters on sEPCR was examined for each time point using a Spearman test (data not shown). No major correlation was found except for platelet count and aPTT at D4. Considering the type of infection, multivariate analysis highlighted a significant impact of gram-negative infection on both sEPCR level and kinetic.

Despite data of sepsis studies large cohorts, the link between severity of coagulation disorders and type of causative microorganism had still remained controversial. . [33 -34 ] We identified a statistically significant difference between D28 survivors and nonsurvivors in terms of sEPCR levels at D2 compared to baseline. This new finding suggests that sEPCR level at D2 may be an early prognostic marker of adverse outcome in septic patients. It could also suggest an implication of elevated sEPCR in the pathogenesis of severe sepsis. While EPCR is considered as a protective molecule , the function of its soluble form remains to be determined. Functionally, sEPCR bind PC and APC with high affinity (Kd [START_REF] Taylor Fb | The endothelial cell protein C receptor aids in host defense against Escherichia coli sepsis[END_REF] = 75nM) and thus may counteract (or balance) the anticoagulant action of mEPCR. On another hand, sEPCR also bind the neutrophil [START_REF] Preston | Selective modulation of protein C affinity for EPCR and phospholipids by Gla domain mutation[END_REF] proteinase PR3 with a similar high affinity, this interaction results in the proteolytic degradation of the receptor . Thus, we can [START_REF] Villegas-Mendez | Proteolysis of the endothelial cell protein C receptor by neutrophil proteinase 3[END_REF] speculate that a significant increase in plasma sEPCR may indeed reflect uncontrolled EC activation and/or irreversible EC injury. This pathogenic link remains to be examined in vitro and in vivo. Whatever the mechanism, a functional impairment of the endothelial protein C activation pathway reflected by an increase in sEPCR level will most probably exacerbate the preexisting state of hypercoagulability in septic patients.

It is to notice that death was associated with higher sEPCR level in septic patients at Day 2 but not at the time of death. Five patients died within the 5 first days of the study. Although it seems difficult to drawn a firm conclusion from only 5 patients, the available values for the last sEPCR dosage before death showed no significant change.

To conclude, severe sepsis, at the onset, only triggers moderate quantitative changes in plasma sEPCR concentration. Our findings also suggest that in pathological conditions such as severe sepsis, an early (at day2 post admission), transient but significant increase in circulating sEPCR may be detrimental. These new findings suggest that measuring sEPCR at Day2 could provide an early biological marker of sepsis outcome.

  Fran ais du Sang (Nantes, France).

Figure 1

 1 Figure 1 Baseline sEPCR in septic patients and controls sEPCR was quantified in blood samples from healthy volunteers (n 40), patients with vasculitis (n 25) and in samples from 40 patients with = =severe sepsis harvested at admission (D1). No significant difference (p 0.37).=

Figure 2

 2 Figure 2 Time-course (from D1 to D5) analysis of sEPCR in septic patients (n 40) = sEPCR was measured daily from admission in ICU (D1) to D5. Statistical difference (p<0.05) is indicated as for group effect (GE) and # " " $ for time effect (TE). ( ) Overall population TE p 0.037, p<0.05 in comparison to D5 . Number of available samples is indicated under " "

]

  December 2004 and September 2005, 82 patients were admitted for severe sepsis in our Medical ICU, 27 patients were not eligible because they had developed first organ dysfunction more than 24h before and 15 patients refused inclusion or delayed their response after inclusion dead line . Thus, the present study includes 40 consecutive adult patients with severe sepsis. Most of them (n 37,

	"	"		=
	93.5 ) were in septic shock at admission but all of them at day 2. The patients ranged in age from 24 to 81 years (58.3 14.4), and 24 (60 % ±	%
	) were female. The mean admission SAPS II score was 51 (SD, 21), and the mean SOFA score at Day1 was 10.5 (SD, 3.4). The overall
	28-day mortality rate was 22.5 . Demographic and clinical characteristics of these patients are summarized in %	Table 1	. The most
	common site of infection was pneumonia (27.5 ). Infecting organism isolation was available for 35 patients (87.5 ) with. a % %
	Gram-negative bacillus for 18 patients (45 ). Hemoculture was positive for 35 of patients.

% %

Acknowledgements:

Funding:

This work was supported by grants from l Agence de Biom decine, La Soci t de N phrologie, l Association pour le D veloppement de la R '


Moussa Chnani
email: moussa.chnani@utbm.fr

Marie-Cécile Péra

Raynal Glises

Jean Marie Kauffmann

Daniel Hissel

Transient thermal behaviour of a solid oxide fuel cell

Keywords: Solid oxide fuel cell, Transient thermal modelling, Fluidic and Electrochemical modelling

A macroscopic model of a short SOFC stack has been developed. The first part of this paper intends to describe a methodology for determining the transient thermal behaviour of the SOFC. A nodal network is used in order to determine the final internal temperatures of the structure. The stack is modelled by one average cell. The cell is divided into several isothermal volumes represented by their central node. The energy balances at each node are developed and solved by Matlab routine. The second part describes a fluidic model in order to compute the partial pressures of chemical species and the output flows. The fluidic model uses electrical/fluidic analogy. Pressure drops in channels are modelled through resistances and the fluid accumulation in the volume is modelled by a capacitor. The next part describes the electrochemical model based on the classical Nernst equation and computation of the overpotential (activation, concentration and ohmic overvoltage). The three submodels are then coupled in order to built a complete modelling of the stack. It has been validated and compared with experimental results on an SOFC stack provided by HTceramix.

1-Introduction

The solid oxide fuel cell (SOFC) is a promising technology. It is highly efficient, tolerant to impurities so it is fuel flexible (methane or even gasoline and diesel), and it can provide internal reforming of hydrocarbon fuels, at least partially. The work presented in this paper is in the frame work of the European project FELICITAS, FP 6, which aims to increase efficiency and life time of FC systems for heavy duty transportation applications (marine, rail, truck). One of the topics is the study of the hybridization of a PEFC and a SOFC. The model proposed here addresses a macroscopic simulation of a SOFC stack. It aims to be included in the simulation of the SOFC and PEFC coupling. The SOFC modeling is an essential tool as fuel cell behaviour is driven by several coupled phenomena: fuel and oxidant species concentration, electrochemical reactions, electric and ionic conduction and heat transfer. A number of detailed theoretical and numerical models of the coupled electro-chemical, thermal, and fluid processes in SOFCs have been already developed, and published. Recently, many papers have modelled the SOFC with Subroutines in a commercial computational fluid dynamic software (CFD). Based on 3-D model and time-dependent [START_REF] Achenbach | Three-dimensional and time-dependent simulation of a planar solid oxide fuel cell stack[END_REF][START_REF] Yakabe | 3-D model calculation for planar SOFC[END_REF][START_REF] Autissier | CFD simulation tool for solid oxide fuel cells[END_REF][START_REF] Sudaprasert | A computational fluid dynamic model of a solid oxide fuel cell, Imperial college of London[END_REF][START_REF] Ferguson | Threedimensional numerical simulation for various geometries of solid oxide fuel cells[END_REF][START_REF] Petruzzi | A global thermo-electrochemical model for SOFC systems design and engineering[END_REF][START_REF] Recknagle | Threedimensional thermofluid electrochemical modelling of planar SOFC stacks[END_REF][START_REF] Khaleel | A finite element analysis modeling tool for solid oxide fuel cell development: coupled electrochemistry, thermal and flow analysis in MARC[END_REF], these models are used to foresee the temperature distribution, gas concentration, velocity profile across the cell and current density. The CFD approach demands a great deal of computational power, especially when simulating a long transient process with a large number of parameters to study. Adding to the computational expense is the very fine discretization required for numerical modelling. This is because of the very high scale ratio of components dimensions in the cell (small thickness of component cell).

Another simplifying model based on 2-D [START_REF] Song | Performance analysis of a tubular solid oxide fuel cell/micro gas turbine hybrid power system based on a quasi-two dimensional model[END_REF] calculates the temperature distribution in the fuel and the air streams along the longitudinal direction. This model considers heat and mass transfer characteristics mainly along the longitudinal direction of the system and the electrochemical reaction in its perpendicular direction.

In [START_REF] David | Reduced-order transient thermal modeling for SOFC heating and cooling[END_REF][START_REF] Chan | A complete polarization model of a solid oxide fuel cell and its sensitivity to the change of cell component thickness[END_REF], a 1-D model approach is developed only along the flow direction and the radiation heat is taken into account. [START_REF] Xue | Dynamic modeling of single tubular SOFC comining heat/mass transfer and electrochemical reaction effects[END_REF][START_REF] Nagata | Numerical analysis of output charateristics of tubular SOFC with internal reformer[END_REF][START_REF] Haynes | Simulating process settings for unslaved SOFC response to increases in load demand[END_REF] use the control volume (CV) approach for the tubular geometry. From this modelling technique, the cell is divided in serial segments by planes perpendicular to fuel flow direction.

Each segment includes: cell CV, anode CV, cathode CV and insulator CV. The heat transfer, species transportation and electrochemical reaction effects are taken into account.

In this paper, three sub-models have been developed (thermal, fluidic and electrochemical) and coupled. The transient thermal model is used to compute the solid and gas temperatures.

The fluidic model calculates the partial pressures of chemical species. The electrochemical model computes the stack voltage and different overvoltages [START_REF] Chnani | Macroscopic Model of Solid Oxide Fuel Cell Stack for Integrating in a Generator Simulation[END_REF]. The figure 1 shows the schematic of stack modelling.

2-Thermal modelling

Thermal failure of components in SOFC is a major obstacle on the path to bringing this technology to commercial viability. The probability of material degradation and failure in SOFCs depends strongly on the local temperature gradients at the interfaces of different materials. Therefore, it is important to accurately predict and manage the temperature fields within the stack, especially near the interfaces.

A SOFC involves complicated heat transfer, species transportation, and electrochemical effects which are highly interactive. In order to make the model tractable while capturing the fundamental dynamic behaviour, a model quasi-2D based on the nodal network of one cell has been developed. This method has already been applied to PEMFC [START_REF] Dumercy | Transient thermal computation of a PEM fuel cell by a nodal modelling[END_REF]. It provides less accurate results than CFD computations [START_REF] Achenbach | Three-dimensional and time-dependent simulation of a planar solid oxide fuel cell stack[END_REF][START_REF] Yakabe | 3-D model calculation for planar SOFC[END_REF][START_REF] Autissier | CFD simulation tool for solid oxide fuel cells[END_REF][START_REF] Sudaprasert | A computational fluid dynamic model of a solid oxide fuel cell, Imperial college of London[END_REF][START_REF] Ferguson | Threedimensional numerical simulation for various geometries of solid oxide fuel cells[END_REF][START_REF] Petruzzi | A global thermo-electrochemical model for SOFC systems design and engineering[END_REF][START_REF] Recknagle | Threedimensional thermofluid electrochemical modelling of planar SOFC stacks[END_REF][START_REF] Khaleel | A finite element analysis modeling tool for solid oxide fuel cell development: coupled electrochemistry, thermal and flow analysis in MARC[END_REF] which are particularly useful to improve the design of the cell. But it require less internal data on the geometry and material and is easier to implement in a global model.

As shown in Figure 2, the cell is divided into several isothermal volumes: anode interconnect, anode channel, electrolyte/anode interface, electrolyte, electrolyte/cathode interface, cathode channel and cathode interconnect [START_REF] Xue | Dynamic modeling of single tubular SOFC comining heat/mass transfer and electrochemical reaction effects[END_REF][START_REF] Nagata | Numerical analysis of output charateristics of tubular SOFC with internal reformer[END_REF]. The cell is submitted to six fundamental heat transfers: 1-Heat transfer due to mass species transportation: For the anode and cathode channel, the heat generation by gas transportation can be represented as:

Q mass,in (A) Q mass,out (A) Q mass,in (C) Q mass,out (C) Q A Q mass, H2 Q cond, Int ae Q cond, e Q conv, iae Q conv, ice Q E Q C Q mass, O2 Q cond, Int ce Q conv, Int-c-ext Q conv, Int-a-ext Anode channel Cathode channel Electrolyte/Anode Interface Electrolyte/Cathode Interface Interconnexion Anode Interconnexion Cathode Electrolyte Q mass,in (A) Q mass,out (A) Q mass,in (C) Q mass,out (C) Q A Q mass, H2 Q cond, Int ae Q cond, e Q conv, iae Q conv, ice Q E Q C Q mass, O2 Q cond, Int ce Q conv, Int-c-ext Q conv,
T c m Q p mass ∆ ⋅ ⋅ = & (1)
Where, m & is the gas mass flow (kg/s), p c is the heat capacity (J/kg.K) and T ∆ is the temperature difference between two nodes [K]. 2-Conduction heat transfer: from the solid to solid structures (interconnects and electrolyte), the conduction heat generation is given by:

T e S Q cond ∆ ⋅ = λ (2)
Where, λ is the material thermal conductivity (W/m.K), e is the volume thickness (m) and S is the volume area (m²).

3-Convection heat transfer: from the solid to gas structures, is given by following expression:

T S h Q conv ∆ ⋅ ⋅ = (3)
Where, h : is the heat transfer coefficient.

4-Radiation heat transfer: from the solid to solid surface structures, it is calculated by: ( )

4 2 4 1 T T S Q conv - ⋅ ⋅ ⋅ = σ ε (4)
Where, ε is the emissivity of the object and σ is the Stefan-Boltzmann coefficient (5.6703.10 -8 W/m 2 K 4 ). 5-The heat generation by chemical reaction: the water formation at anode side is represented as:

S T F I Q f ∆ = 2 (5)
Where, I is the cell current, T is the cell temperature and S ∆ is entropy of the

I R Q A A ⋅ = (6) 2 I R Q C C ⋅ = (7) 2 I R Q E E ⋅ = (8) Where, A R , C
R and E R are respectively anode, cathode and electrolyte ohmic resistance.

The ohmic resistance is calculated using the following expression:

A R δ ρ = (9)
Where, δ is the thickness component, A is the area of component and ρ is corresponding to the material resistivity, calculated with temperature-dependent relation [START_REF] Li | Chyu, Simulation of the chemical/electrochemical reactions and heat/mass transfer for a tubular SOFC in a stack[END_REF] (table1).

Table 1 Component resistivity [START_REF] Li | Chyu, Simulation of the chemical/electrochemical reactions and heat/mass transfer for a tubular SOFC in a stack[END_REF] Electric or ionic resistivity ( cm

Ω ) Anode       - T 1392 exp 00298 . 0 Cathode       T 500 exp 008114 . 0 Electrolyte               - 15 . 1273 1 1 10092 exp 0 . 10 T
The modelling principle by nodal network consists in establishing a co-relation with an electrical network. The considered system is separated into isothermal elements of volume V i with temperature T i . Each element "i" has a heat capacity C i applied to the center i of V i and possibly a heat power generation. The item "i" is called node of the system (figure 3).

The heat transfers by convection, radiation and conduction and the mass transfers as well are taken into account through the matrix G ij . The heat generation by chemical reaction and ohmic losses are located in the vector Q i . The heat balance resulting from the first principle of thermodynamics is applied to the node "i": The nodal modelling is applied at fifteen nodes on cell. The figure 4 shows a 2D model representation of the studied cell. This last is composed with fifteen isothermal control volumes.

i i j j ij i i Q T T G dt dT C + - = ∑ ) ( (10)
The following heat transfer mechanisms and assumptions have been considered:

1. The heat conduction in solid structures (electrolyte and interconnect), it is represented by green thermal resistance.

2. The heat convection between gases and surfaces of solid structures (ex: hydrogen and interconnect surface), represented by blue thermal resistance.

3. The heat radiation between two solid structures (ex: interconnect and electrolyte), represented by red thermal resistance.

4. The heat generation by mass transfer, represented by black thermal resistance.

5. The heat radiation between gas and solid structure is neglected. The energy balance at each node is given (appendix) in order to represent the global energy balance system in the form:

Interconnexion Anode { Anode Electrolyte Cathode T Ain Fuel input Fuel output T ex =T iFurnace T Ia T anode T electolyte R Iaex_conv Cp Ia Cp a Cp elec T Ic R Icex_cond Cp Ic R ina R outa Q r + Q s R C* I² R a2_conv T 2 T 4 R 3e_cond R 4e_cond T cathode T Cin T Cout Air input Air output R Ic_conv Cp C R inC R outC R E* I² Cp 4 T iFurnace =T ex R saex_ray T sa R Iaex_cond R aIex_cond T 1 R aI_conv Cp sa Cp 1 R 12_ray Cp 2 R A* I² T 3 Cp 3 R a2_cond R 4c_cond T 5 Cp 5 R 4c_conv T 6 Cp 6 R Ic_cond T sc Cp sc R Icex_conv R scex_ray R 56_ray T Aout { { { { Interconnexion Anode Interface EA Interface EC a p b c d e f Interconnexion Anode { Anode Electrolyte Cathode T Ain Fuel input Fuel output T ex =T iFurnace T Ia T anode T electolyte R Iaex_conv Cp Ia Cp a Cp elec T Ic R Icex_cond Cp Ic R ina R outa Q r + Q s R C* I² R C* I² R a2_conv T 2 T 4 R 3e_cond R 4e_cond T cathode T Cin T Cout Air input Air output R Ic_conv Cp C R inC R outC R E* I² Cp 4 Cp 4 T iFurnace =T ex R saex_ray T sa R Iaex_cond R aIex_cond T 1 R aI_conv Cp sa Cp 1 R 12_ray Cp 2 Cp 2 R A* I² T 3 Cp 3 Cp 3 R a2_cond R 4c_cond T 5 Cp 5 T 5 Cp 5 Cp 5 R 4c_conv T 6 Cp 6 R Ic_cond T sc Cp sc R Icex_conv R scex_ray R 56_ray T Aout { { { { Interconnexion Anode Interface EA Interface EC
B T A dt dT C p + ⋅ = (11)
Where, T is the temperature vector, p C is the heat capacity matrix, A is the thermal resistance matrix and B is the heat generation vector.

Figure 5 shows the algorithm of the transient thermal model. At the beginning of the simulation, the cell geometry, physical proprieties (specific heat capacity, thermal conductivity, kinetic viscosity…) and initial temperatures are loaded. In the first step, the Reynolds number is calculated and the Nusselt number is empirically calculated by correlation equation. The heat transfer coefficient is computed from the Nusselt number for a forced convection between 2 parallel plates by the following expression:

h D Nu h λ ⋅ = (12)
Where, Nu is the Nusselt number, λ is the thermal conductivity and h D is the diameter of channel.

The heat transfer coefficient calculated is high due to the small characteristic length. The values of h , which have been obtained from this forced convection correlation on the air and fuel sides belong to the range 1000-2000 W/m²K for the fuel and 300-1000 W/m²K for the air.

These results are consistent with some literature estimation respectively:

K m W fuel h ⋅ = 2 / 2987 ) ( and K m W air h ⋅ = 2 / 8 . 1322 ) (
, [START_REF] Xue | Dynamic modeling of single tubular SOFC comining heat/mass transfer and electrochemical reaction effects[END_REF].

For each heat transfer mechanism, the thermal resistances are calculated using the table 2.

( ) ( ) 2 1 2 2 2 1 1 T T T T S R ray + ⋅ + ⋅ ⋅ ⋅ = σ ε Heat mass transfer p mass c m R ⋅ = 1
In the second step, the matrix A , B and p C are calculated. The Matlab's ODE solver routine is applied and the new temperatures are calculated. The boundary conditions are the inlet temperature of the fluid and the inside temperature of furnace surface. The Runge-Kutta methodology is applied to give the final temperatures vector.

3-Fluidic model

The fluidic behaviour in anode and cathode sides has been modelled using an electric fluid analogy [START_REF] Chnani | Macroscopic Model of Solid Oxide Fuel Cell Stack for Integrating in a Generator Simulation[END_REF]. In a formal approach, the flow is related to a current and the pressure is related to a voltage. It is considered that the pressure drop on air side and fuel side is linear with the air flow and fuel flow (table 3) in the considered flow rate range.

C f : fluidic capacity (C f =V/RT) (mbar -1 )
The fluidic model will be based on the following assumptions:

The gases are ideal.

The gas flowing in anode side and cathode side have the same direction (co-flow).

The channels (anode and cathode) have a fixed volume.

Consumption and accumulation of fluids are modelled in one point.

4-Measurements and identification

4-1 Characteristic of the tested stack

Tests have been performed on a SOFC stack in order to identify parameters of the model which has been developed. A test bench has been realized with a 3 cell stack provided by HTceramix company. The stack is fed by hydrogen and air and the gas flow rates are kept constant.

The table 4, shows the characteristics of the HTceramix stack [18].

4-2 Fluidic resistance identification

When the stack is operated at open circuit voltage (OCV) and fed with constant gas flow rate, the consumed gas flow and the flow variation in the electrode volume are negligible. So, the inlet gas flow and outlet gas flow are equal. The input and output resistances are also calculated by following expression:

F P A I Rf A I Rf out in ⋅ ∆ = = = = 2 ) 0 ( ) 0 ( (13

4-3 Fluidic capacity identification

The gases which circulate in the anode and cathode channels are considered ideal and the channel volumes are taken constant. The identification method is presented at the anode. The gas partial pressure at the anode and electrolyte interface (noted catalytic site) can be calculated from the following relationships [START_REF] Chnani | Macroscopic Model of Solid Oxide Fuel Cell Stack for Integrating in a Generator Simulation[END_REF][START_REF] Padullés | An integrated SOFC plant dynamic model for power systems simulation[END_REF][START_REF] Sedghisigarchi | Dynamic and Transient Analysis of Power Distribution Systems With Fuel Cells-Part I: Fuel-Cell Dynamic Model[END_REF]:

a H v a H sc T R n V p ⋅ ⋅ = ⋅ 2 , 2 , (18) ( ) 2 , 2 , 2 , 2 , 2 , 2 , H sc a a H con H out H in H v H v p T R V dt D D D dt D n ⋅ ⋅ = ⋅ - - = ⋅ = ∫ ∫ (19) ∫ ⋅ ⋅ = dt D T R V p H v a a H sc 2 , 2 , 1 (20)
Where,

,H v D

is the hydrogen molar flow in the anodic volume.

Using the fluidic electric analogy (table 3), the fluidic capacity is calculated using the following expression:

a a a f T R V C ⋅ = , ( 21
) c c c f T R V C ⋅ = , (22)

5-Electrochemical model

The SOFC is operated with pure hydrogen and air. So, the electrochemical reactions to be considered are [START_REF] Qi | Dynamic modeling of solid oxide fuel cell: The effect of diffusion and inherent impedance[END_REF][START_REF] Larminie | Fuel Cell Systems Explained[END_REF][START_REF] Chan | Modelling of simple hybrid solid oxide fuel cell and gas turbine power plant[END_REF]:

- -→ + 2 2 2 4 O e O ( 23
) - - + → + e O H O H 2 2 2 2 (24) O H O H 2 2 2 2 1 → + (25)
The stack voltage is computed using the following equation [START_REF] Hall | Transient modelling and simulation of tubular solid oxide fuel cell[END_REF][START_REF] Campanari | Definition and sensitivity analysis of a finite volume SOFC model for a tubular cell geometry[END_REF][START_REF] Qi | Dynamic modeling of solid oxide fuel cell: The effect of diffusion and inherent impedance[END_REF][START_REF] Larminie | Fuel Cell Systems Explained[END_REF][START_REF] Chan | Modelling of simple hybrid solid oxide fuel cell and gas turbine power plant[END_REF][START_REF] Castamagna | Electrochemical model of integrated planar solid oxide fuel cell (IP-SOFC)[END_REF]: ) (

act con ohm cell stack OCV N U η η η - - - ⋅ = ( 26
)
Where cell N is the number of cells in the stack and the other four terms represent respectively, the open circuit voltage, the ohmic, concentration and activation overvoltages.

5-1 Open circuit voltage

The OCV is calculated using Nernst equation:

        + = O H O H p p p F RT E OCV 2 5 . 0 2 2 0 ln 2 (27) F G E 2 0 0 ∆ - = (28)
Where 0 E , the reversible voltage for hydrogen oxidization at ambient pressure, 0 G ∆ represents the standard Gibbs free energy change in the overall cell reaction under standard condition (T=25°C and P=1atm), R is ideal gas constant, p is the partial pressure of the reactants and products and F is the Faraday constant.

The Gibbs free energy at standard conditions may be calculated from the Gibbs free energies of formation of the products and reactants from equation [START_REF] Chan | Modelling of simple hybrid solid oxide fuel cell and gas turbine power plant[END_REF].

5-2 Activation overvoltage

The activation overvoltage describes the resistance to charge transfer at each of the half cells.

It is the principal source of losses at low current densities. The expression of the activation overvoltage ( [START_REF] Chan | A complete polarization model of a solid oxide fuel cell and its sensitivity to the change of cell component thickness[END_REF][START_REF] Chnani | Macroscopic Model of Solid Oxide Fuel Cell Stack for Integrating in a Generator Simulation[END_REF][START_REF] Sedghisigarchi | Dynamic and Transient Analysis of Power Distribution Systems With Fuel Cells-Part I: Fuel-Cell Dynamic Model[END_REF]) is calculated by: The coefficients a and b are functions of temperature and are calculated empirically.

        = 0 i i Ln nF

5-3 Ohmic overvoltage

The ohmic overvoltage is caused by the resistance to the conduction of ions O 2-(through the electrolyte) and electrons (through the electrodes and the current collector) and by the contact between cell components.

The ohmic overvoltage is calculated used the following expression:

I R ohm ohm ⋅ = η (32)
Where, ohm R is the ohmic resistance and I is the stack current.

The ohmic resistance is only function of stack temperature:

( )

1 exp - ⋅ ⋅ = T B A R ohm (33)
Where, T is the stack temperature, A and B are calculated in the linear part of the polarization curves.

5-4 Concentration overvoltage

The concentration overvoltage describes the losses due to gas transport losses in the cell.

They are the principal source of losses at high current densities, it is calculated by the following expression:

        - = L con i i Ln nF RT 1 η ( 34
)
Where:

L i : limiting current [A]

6-Results

In all the tests, the anode side is fed with pure hydrogen and the cathode is fed with air. The gas flows are taken constant at the following values: the hydrogen flow (F inH2 ) is 0.9 Nl/min, and the air flow (F inAir ) is 4.3 Nl/min.

The figure 14 shows the simulation result of the thermal model at very low current (about 1A)

: fifteen node temperatures are given, the name of the nodes are related to the figure 4. The model inputs are: the inlet hydrogen temperature, the inlet air temperature and the furnace temperature, they are respectively 1010K, 974K and 1037K.

The convection heat transfer coefficient of hydrogen is high and the radiation effect between the electrolyte and the interconnect occurs. Hence, in the simulation results, the temperature of the node (T anode ) in the middle of the anode channel (figure 14) is the highest one.

The simulation results show two thermal responses: the zone 1 which consists in the material interconnect (T sa , T Ia , T 1 nodes of the anode interconnect and T sc , T Ic , T 6 nodes of the cathode interconnect) with high thermal conductivity and the zone 2 which consists in the electrolyte and the gas in the channels with low thermal conductivity. The experimental anode and cathode inlet pressures are similar to the simulation (figures [START_REF] Padullés | An integrated SOFC plant dynamic model for power systems simulation[END_REF][START_REF] Sedghisigarchi | Dynamic and Transient Analysis of Power Distribution Systems With Fuel Cells-Part I: Fuel-Cell Dynamic Model[END_REF], and the variation law of fluidic resistances is confirmed.

On the anode side, the water formation reaction increases the partial pressure of water and the reduction of the hydrogen mole number due to the reaction taking place in the anode/electrolyte interface causes a reduction of the hydrogen partial pressure.

In the cathode side, the oxygen is consumed in the chemical reaction which justifies the diminution of the oxygen partial pressure in the cathodic compartment and the nitrogen is not consumed in cathode side, so its partial pressure increases. It can be concluded that the developed model is an interesting tool for the simulation of fuel cell power supply. Due to the compromise which has been chosen between accuracy, fuel cell manufacturer know-how data and computation time, it can be easily implemented in a global modelling with additional components (fuel cell auxiliaries, energy buffers, etc). The first application will be the simulation of the coupling of an SOFC and a PEFC.

/W E C A R R R , ,
∂ ∂ ⋅ ⋅ ⋅ ⋅ = - ⋅ ⋅ + - + + ⋅ ⋅ ⋅ + - ⋅ ⋅ , 1 2 2 , 4 / 2 / ρ λ σ ε Middle anode interconnect temperature ( ) Ia T : ( ) ( ) t T C p b a T T b p a T T b p a Ia I p Ia Ia sa ∂ ∂ ⋅ ⋅ ⋅ ⋅ = - ⋅ ⋅ + - ⋅ ⋅ , 1 1 1 2 / 2 / 2 / ρ λ λ
Temperature between anode interconnect and anode ( )

1 T : ( ) ( ) ( )( )

Figure 1

 1 Figure 1 Schematic of stack modelling

Figure 2

 2 Figure 2 Heat transfer and heat sources on the SOFC cell

Figure 3

 3 Figure 3 Principal of thermal nodal modelling

Figure 4

 4 Figure 4 Thermal model of one cell

Figure 5 1 Figure 5

 515 Figure 5 summarizes the algorithm of the transient thermal model.

Figure 7 Figure 8

 78 Figure 7 Experimental data at OCV

Figure 9 Figure 10 Figure 11

 91011 Figure 9 Polarization curve with increasing and decreasing current at (T a =750°C)

Figures 12 -Figure 12 Figure 13

 121213 Figures 12-13 show the block diagram of the anode fluidic model developed in Matlab Simulink. The hydrogen consumption and the water production flows are computed from the stack current according to the Faraday law.

  The reversible voltage as a function of temperature at cell reaction sites limited to the first order([4,27,28]): The temperature (T ) and partial pressures ( i p ) are respectively calculated by thermal model and fluidic model.

  transfer coefficient n : Number of electron i : Current density [A/cm²] 0 i : Exchange current density [A/cm²]We can write over an empirical equation:

Figure 14

 14 Figure 14 Simulation result of thermal model As temperature measurements inside the stack are not available, the validation of the thermal model is made on the output gas temperature. The figures 15 and 16 show the comparison of the simulation results with experimental data in the same operating conditions than in fig. 14.

Figure 16

 16 Figure 15 Hydrogen outlet temperature validation

Figure 17

 17 Figure 17 Polarization curves validated In order to validate the fluidic model, figures 19-22 show the simulation and experimental

Figure 22

 22 Figure 18 Current profil

R

  Thermal resistance by hydrogen mass transfer between the middle and the output of the cathode K

ρ

  Temperature between cathode interconnect and cathode ( )

Table 2

 2 Thermal resistance calculation

	Heat transfer mechanism	Thermal resistance
	Heat conduction	R cond	= λ	e ⋅	S
	Heat convection	R conv	=	h	⋅ 1	S
	Heat radiation

Table 3

 3 Electric fluid analogy

	Electrical	Fluidic
	Voltage (V)	Pressure (mbar)
	Current (A)	Volumetric flow rate (Nl/min)
	Electrical resistance (Ω)	Fluidic resistance (mbar/Nl.min -1 )

So, each electrode of volume V is modelled with an electric circuit (figure

6

): con : consumed gas flow (Nl/min) P in : inlet gas pressure (mbar) P out : outlet gas pressure (mbar) P sc : pressure (catalytic site sc) (mbar) R fin : fluidic resistance (mbar/Nl.min -1 ) R fout : electrode/electrolyte interface downstream fluidic resistance (mbar/Nl.min

-1 )

Table 4

 4 HTceramix stack specifications and operating conditions

	Number of cells in stack	3
	Active area per cell	50 cm²
	Ideal operating temperature	750°C

  Temperature between anode and anode/electrolyte interface ( )

	b ⋅ 1 λ	a 2 ⋅ /	p	a T : ⋅ ⋅ σ Middle anode temperature ( ) T T p a h T T a I A Ia + -⋅ ⋅ + -1 , 1 ε a	⋅	p	T 2	+	T 1 2	T 2	+	T 1	( T 2	-	T 1	)	=	ρ	⋅	a	⋅	b	/	4	⋅	p	⋅	C	p	,	I	t T ∂ ∂ 1
	h	A	,	I	⋅	a	⋅	p	( T 1	-	T a	)	+	h	A	,	elec	⋅	a	⋅	p	( T 2	-	T a	)	+	m •	A	c	p	,	H	2	( T	T a -Ain	)	+	m •	a	c	p	,	H	2	( T	Aout	T a -	)	+	Q r	+	Q s	+	Q	f	=
	ρ	⋅	a	⋅	c	⋅	p	⋅	C	p	,	A	t T a ∂ ∂

2 T :

(


Solen Quiniou
email: solen.quiniou@irisa.fr

Eric Anquetil
email: eric.anquetil@irisa.fr

In this paper we investigate the integration of a confusion network into an on-line handwritten sentence recognition system. The word posterior probabilities from the confusion network are used as confidence scored to detect potential errors in the output sentence from the Maximum A Posteriori decoding on a word graph. Dedicated classifiers (here, SVMs) are then trained to correct these errors and combine the word posterior probabilities with other sources of knowledge. A rejection phase is also introduced in the detection process. Experiments on handwritten sentences show a 28.5 % relative reduction of the word error rate.

Use of a Confusion Network to Detect and Correct Errors in an On-Line Handwritten Sentence Recognition System 1. Introduction

Most handwritten sentence recognition systems use word graphs to represent alternative sentence hypotheses. The standard Maximum A Posteriori (MAP) decoding is then performed to find the sentence with the highest probability given information from the recognition system and a language model. Unlike this approach which aims at minimizing the sentence error rate, another recent approach from speech recognition tries to minimize the word error rate by using confusion networks [START_REF] Mangu | Finding Consensus in Speech Recognition[END_REF][START_REF] Xue | Improved Confusion Network Algorithm and Shortest Path Search from Word Lattice[END_REF].

Confusion networks where introduced in [START_REF] Mangu | Finding Consensus in Speech Recognition[END_REF]. These networks are used to represent a set of alternative sentence hypotheses and rely on word posterior probabilities. The posterior probability of a word is the sum of the probabilities of all graph paths this word belongs to. These posterior probabilities can then be used to retrieve the best sentence hypothesis or as a confidence measure on words [START_REF] Evermann | Large Vocabulary Decoding and Confidence Estimation Using Word Posterior Probabilities[END_REF]. This confidence measure can also be combined to other knowledge sources in a neural network [START_REF] Kemp | Estimating Confidence Using Word Lattices[END_REF] or a SVM [START_REF] Hillard | Compensating for Word Posterior Estimation Bias in Confusion Networks[END_REF].

In this paper, we integrate confusion networks in our handwriting recognition system to improve its performance.

To our knowledge, confusion networks have not been used yet in the field of handwritten sentence recognition. This confusion network is jointly used with the MAP decoding, already present in our recognition system [START_REF] Quiniou | A Priori and A Posteriori Integration and Combination of Language Models in an On-line Handwritten Sentence Recognition System[END_REF], to detect potential recognition errors. The word posterior probabilities as well as other sources of knowledge are then used to correct these errors. Moreover, a rejection strategy is introduced to reject words that cannot be corrected by the presented approach. This rejection strategy allows the highlight of misrecognized words in an input interface or enables an additional recognition step on these rejected words.

The remaining parts of this article are as follows. In section 2, an overview of the recognition system is given. Confusion networks are then introduced in section 3 while our proposed detection and correction approach is presented in section 4. Finally, experimental results are discussed in section 5 whereas section 6 draws some conclusions.

Overview of the on-line handwritten sentence recognition system

In our sentence recognition system presented in figure 1, each handwritten word of the segmented input sentence W = w 1 . . . w n = w n 1 is first given to our word recognition system RESIFMot [START_REF] Carbonnel | Lexicon Organization and String Edit Distance Learning for Lexical Post-Processing in Handwriting Recognition[END_REF]. This system outputs a list of candidate words which are ordered according to their lexicon score (depending on edit operations during the lexical post-processing step). A graphic score is also added to each candidate word and combines adequation measures between each character and its letter model as well as spatial and statistical information between characters.

A word graph is built using these lists (see part (a) of figure 1) where each node represents a (n-1)-gram w i-1 i-n+1

(and is valuated by the scores of word w i-1 ) and each edge corresponds to the n-gram w i i-n+1 (and is valuated by a language model probability).

The Viterbi algorithm is then performed to find the like-liest path in the word graph (each path corresponding to a sentence), by combining graphic and linguistic information as given by equation 1:

Ŵ = arg max W score(S|W ) + γ log [p(W )] (1)
where score(S|W ) is the score of the signal S for the given sentence W and is estimated by the recognition system (combining graphic and lexicon scores); p(W ) is the a priori probability of the sequence W , given by a statistical language model. A language weight γ is used to balance the influence of the language model against the score from the recognition system [8]. After describing our recognition system, we will present the different steps of the confusion network construction.

Confusion networks

Motivation

The standard approach to sentence recognition is the MAP approach which finds the sentence with the highest posterior probability. However, the most commonly used metric to evaluate the performance of a recognition system is the word error rate. There is thus a mismatch between the recognition approach and the performance metric. Unlike the MAP approach, confusion networks aim at maximizing word posterior probabilities. The nodes in a confusion network represent equivalence classes (confusion sets) i.e. confusions between word hypotheses for a given position in the output sentence and adjacent nodes are linked by as many edges as word hypotheses (see figure 2).

Algorithm

A confusion network is built by first aligning hypotheses from a word graph where each edge stands for a word hypothesis, as can be seen in figure 2(a). Posterior probabilities are then computed for every edge of the graph. Equivalence classes are then initialized such that each class consists of the links with the same starting and ending times as well as the same word label (an edge pruning step can be introduce beforehand to remove links whose posterior probability is too low). Afterward, the intra-word clustering aims at merging classes with the same word label and with overlapping starting and/or ending times. The inter-word clustering is finally done to group together classes corresponding to different words, based on their graphic similarity essentially. This leads to a confusion network as the one from figure 2(b). The hypothesis with the lowest word error rate can then be extracted by picking the word with the highest posterior probability in each confusion set, at each position in the sentence. This hypothesis is called the consensus hypothesis.

In order to focus only on the impact of the confusion network, handwritten sentences, in this paper, are manually segmented to introduce no bias due to incorrect segmentation. The construction of the confusion sets is then straightforward and only word posterior probabilities have to be computed, from the link posterior probabilities.

Word posterior probabilities

The posterior probability of a word is the sum of all link posterior probabilities whose labels are the considering word. The computation of the probability of the k th link of word w i,j can be done efficiently with the forwardbackward algorithm and is given by equation 2:

p(w (k) i,j ) = α(n i-1,k ) p(w i,j |w i-1,k ) γ score(w i+1,k ) δ β(n i,j ) l m r p(w (r) l,m ) (2)
where w (k) i,j is the link corresponding to k th hypothesis of word w i,j , α(n i-1,k ) is the forward probability of node n i-1,k , β(n i,j ) is the backward probability of node n i,j , p(w i,j |w i-1,k ) is the probability of bigram w i-1,k w i,j given by the language model and score(w i+1,k ) is the score given by our word recognition system to word w i+1,k and combines the lexicon and graphic scores presented in section 2 (since our recognition system is non-probabilistic, this score is brought back to range [0:1] and can be assumed to be a likelihood). γ and δ are weights to scale the language model probability and the recognition score respectively and are optimized on a validation set.

The word posterior probability is given by equation 3:

p(w i,j ) = k p(w (k) i,j ). (3)
After presenting confusion networks and the computation of word posterior probabilities, we describe our approach to use a confusion network in conjunction with the word graph, to detect and correct decoding errors.

Error detection/correction using posterior probabilities of recognized words

The detection and eventually correction steps are illustrated in part (c) of figure 1. The confusion network is used to measure the confidence in each word of the best sentence hypothesis given by the Viterbi decoding on the word graph. When an error is detected, a correction step is performed to retrieve the correct word, using this word posterior probability as well as different sources of knowledge.

In the following subsections, we describe our approach to detect and correct errors on the output words. Two types of errors are considered and, for each one, a dedicated classifier is trained to correct the associated error type. An additional rejection strategy is presented in the last subsection.

Mismatch with word whose posterior probability is the highest

In this first type of error detection, the considered output word is detected as potentially misrecognized if its word posterior probability is not the highest one in its corresponding confusion set. In other words, the words from the sentence given by the Viterbi algorithm and from the consensus hypothesis are not the same. To correct the potential error, a dedicated classifier is trained to chose between two words: the recognized word and the one with the highest posterior probability. Three features are considered for each word, namely its posterior probability as well as its normalized lexicon score and its normalized graphic score (see section 2 for a description of these latter scores).

Word with unreliable posterior probability

The second type of detected errors concerns recognized words whose posterior probability is the highest in its confusion set but this probability is below a certain threshold (here, set to 0.8) and is thus considered as unreliable. For the corresponding correction phase, a dedicated classifier is also trained and aims at discriminating the top 2 words of the confusion set (ranked by their decreasing posterior probabilities). The same features as previously are used for each of these two words.

Rejection

In the two correction strategies, we assume that the correct word is one of the two words given as inputs of each dedicated classifier. In fact, the correct word can be either in the remaining words of the confusion set or even not in the confusion set. This simplification was done because most correct words are one of those two words. Indeed, 93.3 % of the words to recognize which appear in the confusion network and which are detected by the strategy presented in section 4.1 are one of the two words considered as inputs of the correction classifier. In the same way, 88.4 % of present words detected by the second strategy (see section 4.2) are one of the two input words. Moreover, there is a problem of data sparsity since by considering more words as inputs of the dedicated classifiers, more training data will be needed to obtain reliable classifiers.

This rejection strategy thus aims at discriminating words where the correct word is one of the two considered words from those where the correct one is not one of them. A new classifier with 6 inputs (corresponding to the 3 previous features for each of the two words) and 2 outputs (acceptation and rejection) is then trained for each detection strategy.

We will compare these strategies in the next section, after describing our data.

Experiments and results

Linguistic and handwritten data

The language model is a bigram model extracted from the Brown corpus [START_REF] Francis | Brown Corpus Manual[END_REF], with the SRILM toolkit [9]. This corpus contains 52,954 sentences (1,002,675 words) where 46,836 sentences (900,108 words) were used to learn the model. The associated lexicon includes 13,748 words.

The handwritten material consists of 118 different sentences from the remaining part of the Brown corpus. These sentences were segmented manually to introduce no bias due to incorrect segmentations.

The training set includes 398 sentences (6,417 words) written by 17 writers (this set is used to learn the classifiers as well as to tune parameters for both the Consensus and the Viterbi algorithms) whereas the test set includes 320 sentences (5,068 words) written by 10 writers. The writers of the test set are different from those of the training set.

Confusion networks

Table 1 compares the results on using the Viterbi algorithm on the word graph or the Consensus algorithm on the confusion network to find the optimal decoding sentence. We remind the achieved rate of the baseline system which uses no language model. The improvement with the Viterbi algorithm is higher than the one with the Consensus algorithm, compared to the baseline system, leading to a 45.7 % reduction of the word error rate on the test set. The fact that the Consensus algorithm performs slightly worse than the Viterbi algorithm can be explained by the already high recognition rate obtained with the Viterbi algorithm. Indeed, the correlation between word error rate and sentence error rate was shown to be much stronger when the word error rate is low [START_REF] Evermann | Large Vocabulary Decoding and Confidence Estimation Using Word Posterior Probabilities[END_REF] so the benefit of switching from the Viterbi algorithm to the Consensus algorithm is reduced. Furthermore, since our word recognition system is not a probabilistic one, the current combination of the graphic model and the linguistic model may not be optimal. In the following experiments, the word posterior probabilities computed on the confusion network are used to evaluate the reliability of the output sentence from the Viterbi algorithm. The quality of word posterior probabilities as confidence scores is evaluated by the normalized cross entropy (NCE) [START_REF] Hillard | Compensating for Word Posterior Estimation Bias in Confusion Networks[END_REF]. The computed NCE is then 0.2. The classifiers used to correct the so-detected errors are Support Vector Machines with gaussian kernels. We chose SVMs because of their capacity to deal with unbalanced classes (in terms of training data) and because of their efficiency.

Decision based on mismatched words

This first detection strategy (see section 4.1) allows the detection of 3.0 % of the words of the test set, which represents 18.1 % of the word errors made by using the Viterbi algorithm. Table 2 gives the word recognition rate over both selected words (ie words selected by this type of decision) and present words (ie selected words where the correct word is one of the two words to classify), for different strategies. The proposed correction strategy leads to a decrease of 43.9 % of the errors among the present words compared to the Viterbi algorithm alone. 3 plots the ROC curve for different rejection classifiers, for each of the two detection strategies. ROC curves shows the compromise between unrejected correct words (TAR) and words to reject and not effectively rejected (FAR). The point M corresponds to the rejection classifier chosen for the current approach. This classifier allows the rejection of 12.0 % of the selected words with a TAR of 99.0 %. The recognition rate is then 49.3 %.

Decision based on unreliable words

This second detection strategy (see section 4.2) allows the detection of 7.7 % of the words of the test set, representing 44.4 % of the errors made by using the Viterbi algorithm. Table 3 shows word recognition rate over both selected and present words, for the different recognition strategies. This correction strategy on unreliable words reduces the error rate over present words by 17.5 %.

Among the rejection classifiers plotted in figure 3, for this detection strategy, we consider two of them (denoted by points U1 and U2 on the figure). This allows us to consider two rejection rates on the words. Thus, with the first rejection classifier, 8.4 % of the selected words are rejected with a TAR of 98.6 % and the recognition rate is then 43.6 %. The second rejection classifier leads to a higher rejection rate of 14.5 % with a TAR of 98.2 %. The corresponding recognition rate decreases a little to reach 43.4 %.

Global decision combination

The combination of the two previous detection strategies enables the selection of 10.7 % of the words in the test set. These selected words represents 62.5 % of the errors made by using the Viterbi algorithm. Table 4 shows the recognition rate over the selected words, the present words as well as over all the words of the test set. The global correction strategy leads to a 90.4 % recognition rate over all the words. In fact, the achievable recognition rate is 91.8 % ie all the present words for each of the two strategies are correctly recognized. Thus, the reduction of the word error rate towards this achievable error rate is 28.5 %. When incorporating the rejection strategies into the global decision (by using rejection classifier M and either classifier U1 or U2), the decrease in the word recognition rate is small. However, the first rejection strategy allows a 13.6 % reduction of all errors (ie word errors as well as correctly rejected words) whereas the second rejection strategy leads to a 17.7 % decrease of all the errors.

Conclusion

In this paper, we have presented the integration of a confusion network in a sentence recognition system where a word graph is already used. The word posterior probabilities computed on this confusion network were then used as a confidence measure on the words of the sentence recognized by the Viterbi algorithm performed on the word graph. Two types of potential errors were thus highlighted and considered. A correction step was also added to correct each type of detected errors, by using SVMs. This correction step allowed the reduction of errors on the words of the sentence from the Viterbi algorithm. Finally, a rejection step was integrated into each of the two decision types to identify words detected as potentially misrecognized but which cannot be corrected by the corresponding correction step. These words can then be highlighted to a user in an input interface or submitted to another recognition step.

Future work will also investigate improvements on the correction of already detected errors as well as a finest detection of potential errors. The sentence segmentation will also be introduced in the confusion network, leading to considering the first steps of the construction of the network.

Figure 1 .

 1 Figure 1. Sentence recognition system.

Figure 2 .

 2 Figure 2. Word graph and corresponding confusion network.

Figure 3 .

 3 Figure 3. ROC curves to reject words in each decision strategy.

Table 1 . Word recognition rates with the Viterbi and the Consensus algorithms.

 1

		training set test set	w.e.r.
				rel. decrease
	Baseline	75.9 %	81.3 %	-
	Viterbi	86.0 %	89.9 %	45.7 %
	Consensus	85.7 %	89.5 %	44.0 %

Table 2 . Word recognition rates for the deci- sion based on mismatched words.

 2

	Strategy	over sel. over pres.
		words	words
	Viterbi	38.0 %	58.2 %
	Detection/correction	50.0 %	76.5 %
	Det./corr. & rejection M	49.3 %	75.5 %

Table 3 . Word recognition rates for the deci- sion based on unreliable words.

 3

	Strategy	over sel. over pres.
		words	words
	Viterbi	41.8 %	74.2 %
	Detection/correction	44.4 %	78.7 %
	Det./corr. & rejection U1	43.6 %	77.4 %
	Det./corr. & rejection U2	43.4 %	76.9 %

Table 4 . Word recognition rates for the global decision.

 4

	Strategy	over all over sel. over pres.
		words	words	words
	Viterbi	89.9 %	40.8 %	69.3 %
	Detection/correction	90.4 %	45.9 %	78.7 %
	Det./corr. & rej. M+U1 90.3 %	45.2 %	76.8 %
	Det./corr. & rej. M+U2 90.3 %	45.0 %	76.5 %


Franc ¸ois BOUTERUCHE Solen Quiniou
email: solen.quiniou@irisa.fr

Eric Anquetil
email: eric.anquetil@irisa.fr

Word Extraction Associated with a Confidence Index for On-Line Handwritten Sentence Recognition

This paper presents an extension of our on-line sentence recognition system by integrating an automatic word extraction mechanism. Our word extraction task is based on the characterization of interstroke gaps, combined to a rejection strategy to evaluate the reliability of the gap classification results. A reconsideration mechanism then used this confidence index to create additional extracted word hypotheses by further controlling the complexity of the recognition task. Different metrics are used to evaluate the impact of this whole word extraction task on the recognition performance, on a set of 395 English sentences.

Introduction

With the rise of new devices like Tablet PC's, users are able to write larger pieces of text. Whereas the recognition of isolated characters and words already achieves high recognition rates, the handwritten text recognition task leads to new challenges. Word extraction is thus an important step since it allows the recognition of isolated words instead of whole text lines. As an on-line handwritten text is represented by a list of chronologically sorted strokes (a stroke is a list of chronologically sorted points, captured between a pen-down and a pen-up), the word extraction task consists in extracting each sublist of strokes corresponding to the words.

The main approach for the a priori word extraction is to identify the intra-word and inter-word gaps between consecutive strokes. The key of this problem is the computation of the distance between two consecutive strokes: it must be invariant to handwriting style variations such as slant, skew, or scale. In [START_REF] Oudot | An Activation-Verification Model for On-Line Texts Recognition[END_REF], the authors work on handwritten manuscript sentences and describe a blank detection task consisting in an inter-stroke gap classification task. They use the bounding box distance as inter-stroke horizontal distance which is heavily subject to handwriting style variations. In [START_REF] Liwicki | Word Extraction from On-Line Handwritten Text Lines[END_REF], the authors use a bounding box distance too, but after preprocessing steps which normalize the signal with respect to slant and skew. Moreover, they determine the lower and upper baselines to perform height normalization. Then, they run an iterative segmentation algorithm adapted from off-line recognition [START_REF] Varga | Tree Structure for Word Extraction[END_REF]. The major drawback of this method is that it can not be used for an "on-the-fly" recognition since the whole text line is used to detect the inter-word gaps.

In this paper, we extend our on-line sentence recognition system [START_REF] Quiniou | A Priori and A Posteriori Integration and Combination of Language Models in an On-line Handwritten Sentence Recognition System[END_REF] by adding an automatic word extraction step. Our word extraction task was conceived to be further extended to an "on-the-fly" recognition. To deal with the possible word extraction errors, we use a confidence index to evaluate the reliability of the extraction. Thanks to it, we control the complexity of the recognition task by limiting the number of extracted word hypotheses to reconsider. Different performance measures are used to evaluate the impact of this complete word extraction task with respect to a manual word extraction task (corresponding to the ground truth).

In Section 2, the recognition system is introduced. The word extraction task is then described in Section 3 while the sentence recognition is presented in Section 4. Finally, experimental results are discussed in Section 5.

Overview of the recognition system

The whole recognition system presented in Figure 1 extends our on-line sentence recognition system previously presented in [START_REF] Quiniou | A Priori and A Posteriori Integration and Combination of Language Models in an On-line Handwritten Sentence Recognition System[END_REF]. The word extraction module (see Section 3) aims at gathering the parts of the input handwritten sentence that correspond to the same handwritten word, to initialize the word graph. The nodes of this graph represent the segmentation frontiers between two consecutive words and the edges stand for the hypothetical handwritten words (initial edges are in bold in Figure 1). The task of the following module (see Section 4) is to create additional edges in the word graph (represented by dotted edges in Figure 1), based on the segmentation scores given by the previous module. Finally, the sentence recognition is performed with the Viterbi algorithm to find the likeliest paths corresponding to the N -best sentence list. For this task, our word recognition system RESIFMot [START_REF] Carbonnel | Lexical Post-Processing Optimization for Handwritten Word Recognition[END_REF] gives a list of 10 candidate words for each handwritten word supported by an edge and a language model is also used to provide the probabilities of word sequences.

Word extraction

Our word extraction scheme consists in an inter-stroke gap classification task. Since our data are English handwritten sentences without any punctuation mark, we consider three kinds of gaps: the intra-word gap (between two strokes from the same word), the inter-word gap (between two strokes from two consecutive words) and the inter-line gap (between two strokes from two consecutive words written on two consecutive lines). As we work on Latin script, the first stroke of a new word is most likely on the right of the last stroke of the previous word. 2). To deal with the problem of slant without applying costly preprocessing steps, we limit the evaluation of the distance to the strokes points contained between the lower and upper baselines. To detect these baselines, we run our detection algorithm on the strokes written before S new . To avoid the skew problem, we only consider the last few strokes written before S new . To determine the number of previous strokes to keep, we use the pertinent downstrokes [START_REF] Anquetil | Perceptual Model of Handwriting Drawing, Application to the Handwriting Segmentation Problem[END_REF]. Our detection algorithm thus needs a group of strokes that represents at least 3 or 4 characters to detect these baselines properly. As a character is composed of 1 to 3 pertinent downstrokes, we keep as many previous strokes to have at least 10 pertinent downstrokes in the group. Thereafter, this group of strokes associated to a S new will be denoted BRG (Baseline Reference Group). In an "on-the-fly" recognition system, the BRG corresponds to a buffer containing the last written strokes. Each newly written stroke is analyzed and added to the buffer. The oldest stroke of the buffer is then removed if it remains at least 10 pertinent downstrokes. The word extraction process can start when at least 10 pertinent downstrokes have been written. Finally, we associate a confidence index to the result of the RBFN: it evaluates the reliability of the first answer. If this confidence index is too low, the second answer is then also considered. To design our confidence index, we use an ambiguity reject [START_REF] Mouchère | A unified strategy to deal with different natures of reject[END_REF]. We learn a threshold on the relative difference dif f 2best between the two best classes. If dif f 2best is below this threshold, the first answer of the RBFN must be reconsidered and additionnal extracted word hypotheses must be generated.

Word graph construction and sentence recognition

The initial word graph is built by considering only the first answer of the gap classification task. Additional extracted word hypotheses are then created using the second answer. To control the size of the final word graph (in terms of number of edges), some limitations are set. Firstly, inter-line gaps are supposed to be correctly identified. The other restrictions aims at dealing with either under-segmentations or over-segmentations.

To deal with potential under-segmentations, the number of potential under-segmented words represented by an edge is set to three i.e. an edge of the initial word graph cannot be separated into more than three parts. Thus, for every edge, the intra-word gaps with a positive ∆x new ref and a dif f 2best below the rejection threshold are sorted according to their ascending dif f 2best . Then, at most the two best intra-word gaps are considered as potential inter-word gaps and additional edges and nodes are created from the current edge, as shown in Figure 3(a) (illustrated by dotted edges and their corresponding nodes).

In the same way, initial edges are limited to be at most an over-segmentation of a word into three parts. Each group of three consecutive initial edges is then considered. When one or the two inter-word gaps have their dif f 2best below the rejection threshold, additional edges are created, as can be seen in Figure 3(b). Moreover, these edges can only be created if their total number of downstrokes is less than 25. The Viterbi algorithm is finally performed on the whole graph to retrieve the N -best sentences Ŵ among all the sentences W k = w k,1 . . . w k,n k , by combining graphic and linguistic information as given by equation 1:

Ŵ = arg max W k score(W k ) = arg max W k n k i=1 score(s k,i |w k,i ) + γ log p(w k,i |w i-1 k,i-n+1 ) + δ (1)
where score(s k,i |w k,i ) is the score of the part of the signal s i corresponding to word w k,i and is estimated by the word recognition system; p(w k,i |w i-1 k,i-n+1 ) is the a priori probability of the word w k,i given its predecessor words w k,i-n+1 . . . w k,i-1 and is given by a statistical language model. The Grammar Scale Factor γ weights the impact of the statistical language model whereas the Word Insertion Penalty δ controls the deletion and insertion of words.

Experiments and results

The language model is a bigram model built with the SRILM toolkit [START_REF] Stolcke | SRILM -An Extensible Language Modeling Toolkit[END_REF], from the Brown corpus [START_REF] Francis | Brown Corpus Manual[END_REF]. This corpus contains 52,954 English sentences (1,002,675 words) where 46,836 sentences (900,108 words) were used to learn the language model. We use the associated lexicon including 13,748 words.

The handwritten material consists of handwritten sentences among the 2,598 remaining ones from the Brown corpus. The training set includes 488 sentences (7,650 words) written by 23 writers (this set is used to learn the RBFN for the inter-word gap classification and the rejection thresholds as well as to tune the values of the grammar scale factor and of the word insertion penalty) whereas the test set includes 395 sentences (6,038 words) written by 15 writers. The writers of the test set are different from those of the training set.

Different measures were used to evaluate the impact of the word extraction task on the performance of the recognition system. The graph density (GD) represents the average number of edges per word and shows the complexity of the word graph. The edge presence rate (EPR) is the percentage of edges in the word graph corresponding to edges in the ground truth word graph. The word presence rate (WPR) stands for the percentage of true words (i.e. words to recognize) which are in the word candidate lists given by the word recognition system. Finally, the word recognition rate (WRR) defines the percentage of correctly recognized words. Table 1 summarizes the comparison between the word extraction associated with different reconsideration strategies as well as relatively to the ground truth. The reconsideration strategies only differ by the percentage of reconsidered gap classification results. The EPR is about 90 % for the word extraction with no reconsideration (and corresponds to the word extraction rate presented in [START_REF] Liwicki | Word Extraction from On-Line Handwritten Text Lines[END_REF]). It exceeds 97 % for the word extraction associated with the other reconsideration strategies. The WPR and the WRR achieve also an absolute rise between 6 % and 7 %. This edge addition obviously leads to an augmentation of the GD but the graph densities remain reasonable. By comparing the different reconsideration strategies, we can see that beyond a certain percentage of reconsidered gap classification results, no significant improvements are obtained. Thus, the reconsideration strategy which allows the better tradeoff between the augmentation of the word recognition rate and the limitation of the graph density is the one where 20 % of the inter-stroke gap classification results are reconsidered. Indeed, the word recognition rate rises from 79.13 % (for the word extraction with no reconsideration) to 85.38 % (for the best reconsideration strategy) which corresponds to a 29.95 % word error rate reduction: relatively to the ground truth, it corresponds to a 71.59 % diminution.

Conclusion and perspectives

In this paper, we have presented an extension of our previous on-line sentence recognition system to a complete recognition system by integrating an automatic word extraction mechanism. Our word extraction strategy leans on the characterization of inter-stroke gaps. A reconsideration step is also added to reconsider not enough reliable gap classification results. This allows the generation of additional extracted words into the word graph on which the sentence recognition is performed. Different reconsideration strategies were thus compared between each other as well as toward the ground truth. This generation of extra hypotheses has lead to an improvement of the recognition system performances, in terms of different indicators. Thus, with the best reconsideration strategy (which reconsiders 20 % of the inter-stroke gap classification results), the word error rate was reduced by 30 % relatively to the ground truth. With our presented word extraction strategy, the recognition system will easily be extended to perform an "on-the-fly" recognition.

Figure 1 .

 1 Figure 1. Sentence recognition system.

  Let's consider a couple of strokes (S ref , S new ), where S ref denotes the last stroke that has been written and classified (also called reference stroke) and S new the next written stroke, in the chronological order, that has to be classified. We propose to use the distance in x-coordinate ∆x new ref between the most-on-the-right point P mtr ref of S ref and the most-on-the-left point P mtl new of S new to characterize the inter-stroke gap between S ref and S new (see Figure

Figure 2 .

 2 Figure 2. Example of ∆x new ref and Baseline Reference Groupe (BRG). Once ∆x new ref has been computed, we use a Radial Basis Function Network (RBFN) to classify the interstroke gap. In addition to the ∆x new ref input, we give to the RBFN three other inputs: the distance between the top of the S new bounding box and the lower baseline (mainly used for the detection of the inter-line gaps), the maximum and the median ∆x new ref in the current BRG. The RBFN outputs are the score obtained by the intra-word, inter-word and inter-line classes. The class with the highest score is then associated to the stroke.

Figure 3 .

 3 Figure 3. Creation of additional edges and nodes, for under-segmentation (a) and over-segmentation (b).

Table 1 .

 1 Performance of the recognition system on the test set.

	Word extraction strategy	GD	EPR	WPR	WRR
	Ground truth	1.00 100.00 % 92.46 % 87.86 %
	Word extraction with 0 % reconsideration	0.99	90.13 %	83.42 % 79.13 %
	Word extraction with 8 % reconsideration	1.41	97.05 %	89.78 % 84.86 %
	Word extraction with 20 % reconsideration	1.80	97.78 %	90.44 % 85.38 %
	Word extraction with 40 % reconsideration	2.18	97.98 %	90.63 % 85.06 %
	Word extraction with 60 % reconsideration	2.38	97.99 %	90.64 % 84.95 %