Pierre Marquet

Franck Saint-Marcoux

Aurélie Prémaud

François-Ludovic Sauvage

Evelyne Jaqz-Aigrain

Christiane Knoop

Yvon Lebranchu

Marco Tiberi

Ingrid Domke

Jean Debord

Aur lie Pr Fran Ois-Ludovic Sauvage

Robert Debr

Performance of the new mycophenolate assay based on IMPDH enzymatic activity for pharmacokinetic investigations and setup of Bayesian estimators in different populations

Keywords: Adult, Anti-Bacterial Agents, pharmacokinetics, Child, Cyclosporine, pharmacokinetics, Dose-Response Relationship, Drug, Drug Interactions, Female, Graft Survival, immunology, Humans, Immunosuppressive Agents, pharmacokinetics, Kidney Transplantation, Male, Mycophenolic Acid, analogs & derivatives, pharmacokinetics, Sirolimus, pharmacokinetics, Tacrolimus, pharmacokinetics, Transplantation, Homologous mycophenolic acid, monitoring, enzymatic assay, LC-MS/MS, Bayesian estimators

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Introduction

Mycophenolate (MPA) is an antiproliferative agent that acts by uncompetitive, reversible and selective inhibition of type II inosine monophosphate dehydrogenase (IMPDH II), a key enzyme in the biosynthesis of purines ( ). MPA is metabolized by de novo 1 glucuronidation primarily to MPA-phenyl-glucuronide (MPAG), which is pharmacologically inactive ( ), as well as to the presumably 2 toxic MPA-acyl-glucuronide (AcMPAG) ( ). A wide interpatient and intrapatient variability was reported for MPA pharmacokinetics ( 3 -5

), leading to the recommendation of therapeutic drug monitoring of mycophenolate mofetil, preferably based on MPA inter-dose area 6 -8 under the concentration-time curve (AUC ) ( , ). However, differences in analytical techniques were found to affect plasma MPA measurement. Previous comparative studies between the enzyme-multiplied immunoassay technique (EMIT, Dade-Behring) and LC-MS/MS ( , ) for the determination of mycophenolate 11 12 (MPA) in renal transplant patients showed that: when mycophenolate mofetil (MMF) was associated with cyclosporine, EMIT significantly overestimated MPA levels in clinical samples (mean 61.4 , SD 57.94 ; median 46.51 , range 27.7 to 422.8 ), with

+ % % % - + %
large variations depending on patients, time elapsed since transplantation, sampling time and concentration levels ( ); when MMF was combined with sirolimus, the EMIT kit gave a significant but lesser overestimation of 18.7 26.8 as compared to LC-MS/MS, also with

± %
variations depending on post-transplantation periods ( ). Therefore HPLC-UV and LC-MS/MS have so far been the standard 12 technologies used for MMF therapeutic drug monitoring. Roche Diagnostics designed and recently released a new MPA assay based on the enzymatic activity of recombinant IMPDH (the pharmacological target of MPA), the Roche (called herein Mycophenolic Acid assay ™ enzymatic MPA assay ), which was recently shown to precisely measure total MPA plasma levels in the range of 0.31 to 15 mg/l with ' '

excellent correlation with HPLC and LC-MS/MS methods and only 5 cross-reactivity with AcMPAG, though it tended to overestimate % MPA concentrations near the quantification limit ( ). 13

A multi-centre, randomized, prospective trial in 137 renal transplant recipients showed that MMF dose adjustment based on de novo MPA AUC resulted in significantly less rejections in the first year post-transplantation ( ). This clinical trial was conducted using 0 12h -14 pharmacokinetic models and Bayesian estimators specifically set up for plasma MPA levels as determined using HPLC ( , ), which 15 16 are now available on the ISBA (ImmunoSuppressants Bayesian Adjustment) website (at ) ( ). https://pharmaco.chu-limoges.fr/abis.htm 17

The larger, comparative, randomized FDCC trial did not show significant differences between the concentration-controlled and the fixe-dose arms, but the renal transplant patients were much more diverse (adults and pediatrics, on cyclosporine or tacrolimus, with MPA measurements made by HPLC or EMIT) and the tools used for dose adjustment (i.e., multilinear regression equations) were probably not as robust and accurate as Bayesian estimation ( ). On top of that, physician s compliance with dose adjustment proposals was only 52 18 estimators developed for LC-MS/MS in the same patients groups.

'

Material & methods

Patients and samples

Plasma samples were collected from 64 patients who gave their informed consent to participate in one of various pharmacokinetic studies approved by regional ethic committees and authorized by the Agence Fran aise de S curit Sanitaire des Produits de Sant , the

ç é é é
French Drug Agency. Sampling times ranged from pre-dose to 6 12 h post-dose, at post-transplant periods varying from day 7 to several years. Twenty profiles came from 20 pediatric renal transplant recipients on cyclosporine (beyond one year post-transplantation), 16

profiles from 10 adult renal transplants on cyclosporine (10 early, i.e. within the first three months post-transplant, and 6 late or stable -periods), 30 profiles from 10 adult renal transplants on tacrolimus (collected at D7, M1 and M3), 28 profiles from 14 adult renal transplants on sirolimus (stable post-transplant periods) and 14 profiles from 10 adult lung transplants on tacrolimus (early and stable post-transplant periods).

All samples were kept frozen for a period of time ranging from 2 months to 2 years before the comparison study.

Analytical methods

The enzymatic MPA assay, based on a two-reagent system, was run on a COBAS INTEGRA 400 system. After sample addition to the reaction mixture, MPA in the sample inhibits IMPDH II that normally catalyzes the conversion of IMP (inosine monophosphate) and NAD (nicotinamide adenine dinucleotide) to XMP (xanthosine monophosphate) and NADH. The enzymatic reaction is monitored by measuring the rate of NADH formation at 340 nm ( ). MPA concentration is inversely proportional to the rate of NADH formation. The measuring 13 range used in this study was 0.4 to 15 mg/L. Using control samples for total MPA at three levels (0.8, 3.5 and 12 mg/L), the intra-assay CV was 1.0 , 0.6 and 1.1 , respectively (n 21).

% % % % =
The LC-MS/MS technique employed was previously described in detail ( ). Briefly, to 100 L of plasma were added 50 L of 11 μ μ indomethacin (internal standard) at 50 mg/L and 250 L of a mixture of acetonitrile and 99 pure formic acid (97/3, v/v). After 0.05 mg/L and the limit of quantitation (LLOQ) 0.1 mg/L. Linearity was verified up to 30 mg/L (r 0.999). The within-day and = between-day precision (CV < 10 and < 15 , respectively) and accuracy (mean bias < 7 for both) were satisfactory over the % % % % calibration range. Samples with MPA concentration > 30 mg/L (upper limit of quantitation) were diluted 1/2 with blank human plasma and re-analyzed.

Method comparison

The three QC samples provided by Roche Diagnostics for the enzymatic MPA assay and two commercial QC samples for MPA monitoring (ChromSystems, level I: 1.8 mg/L; and level II: 4.86 mg/L) were analyzed with each batch of patients samples using both ' assays, for cross-checking. Furthermore, six external quality control samples from the International Mycophenolate Proficiency Testing Scheme (3 pools of blank plasma spiked to a known concentration of MPA and 3 pools of plasma from treated patients) were purchased from Analytical Services International (London, UK) in sufficient volumes and analyzed by both methods with 15 different batches of patients samples.

'

Patients plasma samples were thawed in batches and analyzed in parallel, on the same day, with both methods. For the enzymatic ' MPA assay, samples with MPA concentration above 15 mg/L (upper limit of quantitation) were diluted 1/4 with blank human plasma and re-analyzed. For each PK profile, the two PK models (i.e., the two-compartment model with one gamma law and the one-compartment model with two gamma laws) were applied and the best one was selected based on the lowest Akaike criterion ( ), calculated as follows: 19

PK modeling and development of Bayesian estimators

where is the value of the objective function at minimum and p the number of parameters in the model.

Φ min

Using the appropriate pharmacokinetic model and the final set of population parameter estimates (mean, standard deviation and correlation matrix), maximum a posteriori Bayesian estimators (MAP-BE) were developed as previously described ( , ), for each 16 20 group of patients defined by the associated immunosuppressant and post-transplantation period. Every combination of 3 sampling times within the first 3 hours post-dose was tested for MAP-Bayesian forecasting.

Statistical analyses

Method comparison was performed globally, as well as separately for the different sub-populations. Correlation analysis was conducted using the non-parametric Passing-Bablok method ( ). The relative difference was calculated as (enzymatic MPA 21 assay-LC-MS/MS)/LC-MS/MS, and normalized relative difference as (enzymatic MPA assay-LC-MS/MS)/mean (enzymatic MPA assay and LC-MS/MS).

For each individual post-transplantation period, the best limited sampling strategies (LSS) for Bayesian estimation were selected on the basis of: (i) the best squared correlation coefficients (r ); and (ii) the lowest bias between observed and estimated AUC (AUC 2 0 12h

being the main index targeted). Then, for practical reasons, a common LSS over the 3 periods was sought and evaluated. The whole procedure was repeated for MPA PK profiles generated using the enzymatic MPA assay and LC-MS/MS.

The influence of age, transplanted organ, associated drug and post-transplantation period on the relative differences between the two techniques was tested using one-way ANOVA, then two-by-two comparisons for the influence of the associated immunosuppressive drug by the Scheffe test.

Finally, the PK parameters obtained with the enzymatic MPA assay and LC-MS/MS at different post-transplantation periods on the one hand, and the respective Bayesian AUC estimates on the other hand were compared using paired t-tests.

Results

The cross-checking of internal quality control samples analyzed routinely with the batches of patients samples showed that there was ' no systematic difference between the enzymatic MPA assay and LC-MS/MS and that the inter-assay CVs obtained with the former were always less than those obtained with the latter ( ). Moreover, repeated analysis ( LC-MS/MS), with r 0.9839 and more than 95 samples within 20 to 30 ( ).

= % -% + % figure 1

Though samples above 15 mg/L (n 47) were determined with the same accuracy and precision after dilution with blank plasma as = samples in the linearity range ( ), method comparison within the different sub-groups defined by age, transplanted organ, figure 1 co-administered immunosuppressant and post-transplantation period (

) were limited to the 818 samples with concentration values table III within the linearity range of the enzymatic MPA assay (0.4 to 15 mg/L), in order to avoid sample dilution as a confusing factor. They showed that the agreement between the two methods was excellent in all cases, with slightly though significantly higher overestimation of the enzymatic MPA assay in adults than in children, in patients on cyclosporine than in those on tacrolimus or sirolimus, and in the stable than in the early (i.e., within the first three months) post-transplantation periods (

). In contrast, there was no significant difference table III between lung-and kidney transplant recipients.

In the study database, 68 PK profiles containing at least 10 concentration-time points could be used to develop PK models and Bayesian estimators. These PK profiles analyzed with both the enzymatic MPA assay and the LC-MS/MS technique were adequately fitted using the same types of PK models as those previously reported for MPA ( ), though with a different equation for the analytical error, 16

Discussion

The new enzymatic MPA assay tested showed excellent correlation with LC-MS/MS for the determination of total MPA in plasma of adult or pediatric, renal or lung transplant patients under cyclosporine, tacrolimus or sirolimus in the early or stable post-transplantation periods. A negligible systematic bias of about 6 was found between the two techniques when analysing spiked plasma samples

+ %
routinely, with the enzymatic MPA assay showing better precision.

Full PK profiles may result in very low (down to 0.017 mg/L) to quite high (up to 33.4 mg/L) plasma levels, some of which were out of the analytical range of the enzymatic MPA assay. However, very low concentrations were mainly found for trough levels obtained very early after transplantation, when it is now widely accepted that trough levels have limited significance, at least for MMF dose adjustment (

). In the present as well as in previous studies ( , , ), we proposed Bayesian estimators of MPA AUC based on plasma 10 14 16 17 0 12h

samples collected at approx. 20 min, 1h and 3h post-dose, times at which MPA plasma levels were almost always above the LLOQ of the enzymatic MPA assay in our hands (0.4 mg/L). Above this LLOQ, the enzymatic MPA assay gave results very close to those of LC-MS/MS in all patients groups as determined by age, transplanted organ, co-administered immunosuppressant and post-transplantation period, though with slight overestimation of MPA plasma levels in patients on cyclosporine (mean 10.7 ). This last finding is in % agreement with those of previous reports comparing EMIT to LC-MS/MS, which showed that EMIT overestimated MPA plasma levels more in patients co-administered cyclosporine ( ) than sirolimus ( ) or tacrolimus ( , ), although overestimation was then globally 11 12 23 24 much higher with EMIT than with the enzymatic MPA assay herein. This might be due to the inhibition of the biliary excretion of MPA phase II metabolites, by cyclosporine but not tacrolimus or sirolimus ( ), resulting in an increase in plasma concentrations of these 25 -27 metabolites, mainly AcMPAG. However, it was shown that MPAG did not inhibit IMPDH, while MPA-acyl-glucuronide (AcMPAG) exhibited only 5 of MPA inhibition activity on the recombinant enzyme when incubated alone ( ), and even less when co-incubated % 13 with MPA ( ). However, the overestimation of actual MPA levels by the enzymatic MPA assay found in patients on cyclosporine should 28 be of little clinical significance, so much so that this overestimation is proportional across the linearity range and with time post-dose, contrary to that of EMIT ( ). It should also be noted that a previously published inter-laboratory validation of the enzymatic MPA assay, 11

which was conducted after the present study and in which we also participated, found no significant overestimation, whether in patients on cyclosporine or on tacrolimus ( ). This could be due to the nature of the kit itself, as the beta-version used in the present study was 13

slightly different from the commercial version employed in the interlaboratory validation study.

Two different PK models with either one or two gamma laws, previously developed for renal transplant patients ( ) were used to fit 15 the present database. As raw data showed that patients could exhibit PK profiles with either one or two peaks, the best model was selected for each profile based on the Akaike criterion (a selection procedure now automatically applied to all three-point profiles sent to the ISBA website).

Significant differences in the PK parameters were found between LC-MS/MS and the enzymatic MPA assay, highlighting that analytical techniques not only impact the actual levels measured and the residual error of the models, but also the distribution of PK parameters in the population. This advocates the need for specific (or possibly adapted) models for pharmacokinetically-guided TDM when different analytical techniques are employed, even when they give close results as in the present study.

Bayesian estimators derived from these models were able to accurately estimate MPA AUCs when measured with the enzymatic MPA assay (i.e., more than 80 of the AUC estimates were within 20 of the actual values), with similar efficiency at all post-transplantation % ± % periods and for all three associated immunosuppressive drugs. When comparing Bayesian AUC estimates to those obtained with LC-MS/MS, significant although limited mean differences were observed, mainly in patients on cyclosporine or sirolimus. Also, the distribution of the AUC relative differences with respect to LC-MS/MS ( ) was very similar to that of the raw concentration data ( figure 4 ). This should not be of clinical significance, in as much as the commercial enzymatic MPA assay apparently presents less figure 1 overestimation than the beta version used in the present study (see above). This should not affect the accuracy of the Bayesian estimators developed here, which are more sensitive to curve shapes (hence PK parameters) than to absolute concentration values. These tools were added to the ISBA website (https://pharmaco.chu-limoges.fr/abis.htm) to allow dose adjustment of MMF when measured using the Roche Diagnostics total MPA kit and have been used successfully since.

Ackowledgements:

This study was sponsored by Roche Diagnostics.

We express our thanks to: Prof. Yannick Le Meur, Dr Jean-Philippe R rolle and Dr Jean-Christophe Szelag, who enrolled many patients in all é the clinical trials mentioned in this paper; Laetitia Vignaud, Jean-Louis Dupuy, Karine Delaune and Franck Giraudie for excellent technical assistance; Monika Widmann, Roche Diagnostics GmbH Mannheim for technical support; and Karen Poole for English revision.

References:

1

1 -

 1 and centrifugation, 3 L of the supernatant were injected into a Nucleosil C , 5 m (150 1 mm ID.) column. The mobile μ 18 μ × phase, delivered at a flow-rate of 50 L.min , was a gradient of acetonitrile in 5mmol/L, pH 3.0 ammonium formate. Detection was μ performed using a 2000 Q-TRAP tandem mass-spectrometer (Applied-Biosystems/Sciex, Foster, CA, USA) in the negative ion, multiple reaction monitoring mode using the following transitions: MPA (m/z 319 191 for quantification and m/z 319 275 for -→ --→confirmation) and indomethacin (m/z 356 312 for quantification and m/z 356 297 for confirmation). The limit of detection was

  Two previously published PK models able to fit MPA absorption profiles were tested ( ): a two-compartment open model with first 15 order elimination and a single gamma input to describe the absorption phase; and a one-compartment open model with first order elimination and a sum of two gamma distributions to describe the absorption phase, theoretically able to describe the double-peak concentration-time curves frequently observed with MPA. Population parameters were estimated using the iterative 2-stage method (ITS) as implemented in an in-house computer program. Bayesian fitting of the PK model to each individual data set (all available concentrations) employed the simplex algorithm to minimize the individual objective function value: where C denotes an observed concentration, S its standard deviation, E the corresponding theoretical concentration, the vector of i i i θ fitted parameters, the mean parameter values in the reference population, and the inverse variance-covariance matrix. The symbol T μ Σ 1 denotes matrix transposition. The calibration experiments showed that S could be expressed as a power function: S 0.015 C , where i i = × i 1.2 C and S are in mg/L. The program used the individual parameter estimates together with their variance-covariance matrix to generate a i i new set of population parameter estimates. These population estimates were then used as Bayesian priors and refined by successive population iterations until convergence.

-

  All statistic analyses were performed using Statview 5.0 (SAS Institute Inc., USA).

  figure 3 obtained using the enzymatic MPA assay or LC-MS/MS was 12.3 15.3 on average. The individual relative differences were highest ± % and significant in patients given cyclosporine (13.3 20.4 ; p<0.01), moderate and still significant in those on sirolimus (10.1 10.8 ; -% -% p<0.01), lower and not significant in patients given tacrolimus (4.1 9.1 ; n.s). shows the Bland-Altman ( ) representation of -%

Figure 1

 1 Figure 1 Comparison of the Roche enzymatic MPA assay run on the COBAS INTEGRA system with LC-MS/MS using plasma samples with MPA concentration > 0.4 mg/L, as determined by the enzymatic MPA assay. A) Passing-Bablok correlation analysis. B) Normalized relative differences (i.e., (enzymatic MPA assay LC-MS/MS)/mean of (enzymatic MPA assay and LC-MS/MS) plotted against increasing mean concentration, as represented by sequence number.

Figure 2 Figure 3

 23 Figure 2 Bias of the Bayesian estimates of MPA AUC obtained using the 20 min-1h 3h sampling schedule with respect to the true , trapezoidal 0 12h --" " AUC sorted out by: A) associated immunosuppressant; and B) post-transplantation periods. 0 12h -

Figure 4

 4 Figure 4 Bland-Altman representation of the relative bias of MPA Bayesian estimates obtained using concentrations measured at approx. 20 min, 1h and 3h post-dose with the enzymatic MPA assay as compared to LC-MS/MS.

'

  15 or 16 replicates) of spiked or patients samples table I from the Mycophenolate International Proficiency Testing Scheme showed a mean difference 6 between the two assays and lower CV ≤ %values with the enzymatic MPA assay than with LC-MS/MS, except for the spiked sample at the highest concentration (). The

	%	table II
	MPA concentrations as measured by LC-MS/MS in 894 patients samples taken over dosing intervals ranged between BLOQ (i.e., below
	0.1 mg/L) and 33.4 mg/L. The concentration measured by the enzymatic MPA assay was lower than 0.4 mg/L, limit of quantitation of the
	assay, in 29 samples. When comparing the results obtained for the remaining 865 patients samples, the mean overestimation of the '
	enzymatic MPA assay was 7.8 12.7 (median 7 , range 19.1 to 54.5 ), translating into mean 6.8 11.7 (median 6.8 , range %± % % -+ % = %± % %	-
	21.2 to 42.8 ) for the normalized relative difference (enzymatic MPA assay LC-MS/MS)/mean (enzymatic MPA assay and + % -

  . Ransom JT . Mechanism of action of mycophenolate mofetil . Ther Drug Monit . 1995 ; 17 : 681 -684 2 . Bullingham RES , Nicholls AJ , Kamm B . Clinical pharmacokinetics of mycophenolate mofetil . Clin Pharmacokinet . 1998 ; 34 : 429 -455

Table II

 II Analysis of blinded control samples from the Mycophenolate International Proficiency Testing Scheme ( ) by the enzymatic MPA assay and LC-MS/MS in parallel. www.bioanalytics.co.uk

			M22A Patient pool	M23A Patient pool	M30A Spiked sample	M30 B Spiked sample	M31A Patient Sample	M32 B Spiked sample
			Enzymatic MPA		Enzymatic MPA		Enzymatic MPA		Enzymatic MPA		Enzymatic MPA		Enzymatic MPA
			assay	LC-MS/MS	assay	LC-MS/MS	assay	LC-MS/MS	assay	LC-MS/MS	assay	LC-MS/MS	assay	LC-MS/MS
	Number	of	16	16	16	16	16	16	16	16	15	15	15	15
	replicates
	Median (mg/L)	1.55 (1.45 1.62) -	1.58 (1.34-	1.58 (1.50 1.64) -	1.51 (1.30-	3.66 (2.60 3.78) -	3.58 (2.92-	1.13 (1.06 1.20) -	1.09 (0.90-	1.86 (1.80 1.91) -	1.75 (1.58-	10.47 (10.08-	10.65 (9.23-
	(range)			1.76)		1.86)		3.88)		1.20)		1.95)	14.14)	11.30)
	Mean (mg/L)		1.55	1.57	1.57	1.53	3.59	3.52	1.13	1.06	1.85	1.76	10.89	10.40
	CV%		2.8	8.7	2.67	10.7	7.6	9.4	3.8	8.4	1.7	6.0	12.2	6.9

[START_REF] Knight | Does the Evidence Support the Use of Mycophenolate Mofetil Therapeutic Drug Monitoring in Clinical Practice? A Systematic Review[END_REF]

[START_REF] Knight | Does the Evidence Support the Use of Mycophenolate Mofetil Therapeutic Drug Monitoring in Clinical Practice? A Systematic Review[END_REF]

[START_REF] Knight | Does the Evidence Support the Use of Mycophenolate Mofetil Therapeutic Drug Monitoring in Clinical Practice? A Systematic Review[END_REF]

[START_REF] Knight | Does the Evidence Support the Use of Mycophenolate Mofetil Therapeutic Drug Monitoring in Clinical Practice? A Systematic Review[END_REF]

[START_REF] Knight | Does the Evidence Support the Use of Mycophenolate Mofetil Therapeutic Drug Monitoring in Clinical Practice? A Systematic Review[END_REF]

[START_REF] Knight | Does the Evidence Support the Use of Mycophenolate Mofetil Therapeutic Drug Monitoring in Clinical Practice? A Systematic Review[END_REF]

10

Table I

Cross-checking of internal quality controls analysed using the enzymatic MPA assay and LC-MS/MS in parallel.

Method


Luis Felipe

Fonseca Dias

Camille Jouvaud
email: camille.jouvaud@cea.fr

Christophe Delaveaud
email: christophe.delaveaud@cea.fr

Herve Aubert
email: herve.aubert@toulouse-inp.fr

Polarization Conversion from a Two-Port Impedance Loaded Tag

Keywords: electromagnetic backscattering, passive scatterer, polarization conversion, polarization diversity

The electromagnetic clutter mitigation is increasingly demanded for achieving the indoor identification and longrange reading of wireless and passive sensor tags. In this paper, a new Polarization Diversity scheme is proposed to reduce the clutter and potentially, to increase the reader to tag separation distance. The proposed wireless tag is a two-port patch antenna loaded by proper passive impedances. When illuminated by a circularly polarized electromagnetic field, the proposed tag backscatters a linearly or circularly polarized field, depending on the choice of four passive load impedances. This polarization conversion is then easily controlled, and can be advantageously implemented to improve the existing wireless systems by reducing the line-of-sight environment clutter and, from this, increasing reader-to-tag separation distance.

I. INTRODUCTION

The advent of 5G has solidified the notion of Internet of Things and the increase of the number of wireless sensors sharing a common space. As consequence, mitigating the electromagnetic clutter is necessary to achieve long-range detection and reading of such sensors, such as RFID sensor tags or so-called antenna sensors [START_REF] Paul | Survey of RF Communications and Sensing Convergence Research[END_REF].

Techniques for remotely and wirelessly interrogating passive sensors or tags can be mainly divided into two classes: In the first class, the frequency of the electromagnetic field backscattered by the sensor differs from the frequency of the incident field [START_REF] Pons | Electromagnetic Transduction for Wireless Passive Sensors[END_REF]. Still in this line, another well-known technique is based on the frequency hopping, in which the frequency used in the wireless link is outright shifted [START_REF] Sabesan | Wide Area Passive UHF RFID System Using Antenna Diversity Combined With Phase and Frequency Hopping[END_REF], [START_REF] Zhu | A Compact, Passive Frequency-Hopping Harmonic Sensor Based on a Microfluidic Reconfigurable Dual-Band Antenna[END_REF]. In the second class, the polarization of the electromagnetic field backscattered by the sensor differs from the polarization of incident field. For instance, Circular-to-Circular Polarization (CP-to-CP) conversion can be used for increasing by over 17% the reading range (i.e., the separation distance between the reader and the sensor) compared with the well-known Linearto-Linear Polarization (LP-to-LP) conversion [START_REF] García | Coverage and read range comparison of linearly and circularly polarised radio frequency identification ultra-high frequency tag antennas[END_REF]. The use of Vertical-to-Horizontal (V-to-H) or Horizontal-to-Vertical (Hto-V) polarization conversion allows reaching reading ranges exceeding 50 m [START_REF] Henry | Long-Range Wireless Interrogation of Passive Humidity Sensors Using Van-Atta Cross-Polarization Effect and Different Beam Scanning Techniques[END_REF], and the use of CP antennas for wireless indoor communication provides better overall performance by mitigating the electromagnetic clutter in indoor applications [START_REF] Rappaport | Wide-band microwave propagation parameters using circular and linear polarized antennas for indoor wireless channels[END_REF], notably for line-of-sight channels, which offer better crosspolarization discrimination. Recent works proposed to use depolarizing tags to compensate misalignment issues between tag and reader [START_REF] Costa | Chipless RFIDs for Metallic Objects by Using Cross Polarization Encoding[END_REF] and even exploit the misalignment to their advantage [START_REF] Vena | A Depolarizing Chipless RFID Tag for Robust Detection and Its FCC Compliant UWB Reading System[END_REF]. However, no practical solutions based on the polarization diversity and using impedance loaded tags have been reported to date. Recently, the Authors proposed a new technique [START_REF] Fonseca Dias | Linearto-Circular Polarization Conversion from Impedance Loading of Single-Port Patch Antennas[END_REF] based on the control of the polarization of the electromagnetic field backscattered by passive single-port antennas. The proof-of-concept was established only from theoretical considerations and illustrated from preliminary simulation results. In the present study, the technique is extended to two-port antennas in order to achieve four different polarizations of the backscattered field from an incident circularlypolarized electromagnetic field. Measurement results obtained from a loaded two-port microstrip patch antenna acting as a tag (or a passive scatterer) are provided for experimental validation purpose.

The paper is organized as follows. Section II describes the two-port patch antenna and passive impedances connected to the two input ports of the antenna. Section III details the experimental setup and the calibration process applied for measuring the Radar Cross Section (RCS) of the tag. Section IV reports the experimental validation of the proposed control of the polarization of the electromagnetic field backscattered by the tag. Finally, conclusions and perspective outlines are provided in Section V.

II. TWO-PORT IMPEDANCE LOADED TAG A. Two-Port Patch Antenna

The proposed antenna geometry of the tag is shown in Fig. 1. The tag is a microstrip patch antenna on a combination of two types of substrates: FR-4 and air, with ε r equal to 4.3 and 1, respectively, designed to operate at 2.45 GHz. The patch itself is a thin copper square (0.37λ x 0.37λ surface, 35 µm thickness) cut from a bigger square copper board (0.65λ x 0.65λ x 0.007λ). The ground plane is a copper board with the same dimensions as the first board. As illustrated in Fig. 1b, the two copper boards are superposed and held apart by nylon (ε r = 3.5) spacers, creating an air gap of thickness t air . Both conducting faces are directed outwards. The antenna's ports are physically implemented by two transversal feeding probes, positioned at the points x f and y f (see Fig. 1a).

Antenna measurements are performed in an anechoic chamber, and the full-wave electromagnetic simulations are exe- cuted by the 3D simulation suite MWS CST. It can be observed in Fig. 2 that the simulated input reflection coefficients at the two input ports are in very good agreement with the measured ones. A good impedance matching is achieved over the bandwidth of 5% of the operating frequency (2.45 GHz). As shown in Fig. 3, an excellent agreement is obtained between the simulated and measured co-polar antenna gain when both input ports are separately fed (when one port is excited, the other port is loaded by a 50 Ω impedance). The broadside gain is about 8 dBi at 2.45 GHz.

B. Passive Two-Port Circuit for loading the Antenna

The structural scattering is mostly dependent on the geometry of the antenna, and for this reason, a Coplanar Transmission Line (CPTL) is used as the two-port circuit of the scatterer under study. The transmission line consists of a central conductor, of length l cp and width w ser , separated on both sides by a narrow air gap (g) from the antenna ground. The width w ser has been designed so that the line's resistance coincides with the reference impedance Z 0 = 50 Ω.

For the load circuits, we propose two setups adding lumped resistances on the transmission line. The first configuration will be called the "series" setup, illustrated in Fig. 4b. This setup consists of replacing a part of the central conductor to a lumped resistance, represented as a red box and labeled as resistance 1 in Fig. 4b. The second setup, which will be called as the "parallel" setup, consists of a balanced bridge between central conductor and ground using equal lumped resistances. Both resistances are indicated as red boxes, labelled as resistance 1 and resistance 2, as shown in Fig. 4c. In both setups, the lumped elements are positioned in the middle of the line, or at l cp /2. Fig. 4a displays the back view of a realized twoport patch scatterer with the "series" line setup highlighted.

III. EXPERIMENTAL SETUP FOR THE RCS MEASUREMENTS

In this section, we describe the experimental setup used to charactere the electromagnetic backscattering of the tag, and we briefly describe calibration process used for measuring the backscattered field of the tag.

The polarization conversion achieved by the tag, loaded by proper passive impedances (see Section IV), is validated here from measurement results obtained in an anechoic chamber. Identical transmitting (Tx) and receiving (Rx) horn antennas (about 10 dBi of gain in the frequency band of interest) are used for the measurements. The experimental configuration is bistatic, as the Tx-and Rx-antennas are not co-located. The Tx-antenna is vertically polarized, while the orientation of the Rx-antenna is mechanically controlled to measure the backscattered electromagnetic field for different polarization modes. We derive the so-called measured backscattering matrix [S m ] (see [START_REF] Wiesbeck | A complete error model for free space polarimetric measurements[END_REF]) from these results. The tag is called in this Section the Scatterer Under Test (SUT). SUT, Tx-and Rx-antennas are placed half-height up the anechoic chamber. The separation distance between the Tx-and Rx-antennas is 0.7 m (5.7λ), while the distance between these two antennas and SUT is 3.35 m (far-field condition). Moreover, the electromagnetic field transmitted by the Tx-antenna is normally incident upon the SUT planar surface, and the bistatic angle is 11 • . The SUT backing is composed of a fixed plastic base to monitor the azimuth angle of the scatterer, and is placed on a foam support, as shown in Fig. 5. A rotating plastic hollow disk is used to hold the antenna and to control the relative incident field polarization to measure the backscattering matrix [S m ]. The experimental setup offers a tunable measurement bandwidth from 1.5 GHz to 6 GHz, with the frequency step of 1 MHz. The setup is calibrated from Single-Reference Calibration (SRC) technique proposed in [START_REF] Wiesbeck | A complete error model for free space polarimetric measurements[END_REF], and adapted to our need (bistatic configuration) [START_REF] Kahny | Calibration of bistatic polarimetric radar systems[END_REF]. The goal of this calibration step is to derive the so-called calibrated backscattering matrix [S c ] by compensating the eventual distortion due to the electromagnetic propagation on the measured backscattering matrix [S m ] [13]. The SRC technique is preferred here to the standard calibration process (see, e.g., [START_REF]Radar cross section measurements[END_REF]) because it is more time-efficient, while ensuring the similar measurement accuracy of RCS.

IV. POLARIZATION CONVERSION FROM IMPEDANCE LOADING OF THE TAG

In this section, we show that it is possible to control the polarization of the electromagnetic field backscattered by the impedance loaded tag of Section II, when the tag is illuminated by a circularly polarized field. The impedance loads have been determined from the extension to two-port antennas of the electromagnetic analysis reported by the Authors in [START_REF] Fonseca Dias | Linearto-Circular Polarization Conversion from Impedance Loading of Single-Port Patch Antennas[END_REF] for modeling single-port antennas. To achieve the Left-Handedto-Right-Handed Circular Polarization (LHCP-to-RHCP) con-version, "parallel" resistance 1 and resistance 2, defined in Subsection II-B, are both equal to 0 Ω (jumpers). To achieve the LHCP-to-LHCP conversion, "series" resistance 1 is equal to 20 Ω. To obtain the first CP-to-LP conversion, "parallel" resistance 1 and resistance 2 are both equal to 56 Ω and finally, to achieve the second CP-to-LP conversion, the resistance load of the "series" resistance 1 is equal to 120 Ω.

The results reported in this Section are derived from the calibrated backscattering matrix [S c ], when the tag is illuminated by a LHCP electromagnetic field. The Axial Ratio [START_REF] Balanis | Antenna Theory[END_REF] of the field backscattered by the tag is measured to determine the polarization (linear, elliptical or circular) of this field. When the backscattered field is circularly polarized at the measured operating frequency (2.46 GHz), the phase difference between the vertical and horizontal components of this field is measured in order to discriminate between Left-Handed (90 • ) and Right-Handed (-90 • or 270 • ) circular polarizations. When the backscattered field is linearly polarized, the magnitude of the co-and cross-polarized components indicates the polarization isolation of each LP state.

A. LHCP-to-RHCP Conversion

The LHCP-to-RHCP conversion is achieved by soldering jumpers (0 Ω resistances) to connect the two sides of the ground to the central conductor, in the setup defined as "parallel", see Fig. 4c.

Fig. 6 shows stable Axial Ratio over the frequency band, which indicates that the metallic plate (generating the structural backscattering mode) has a predominant influence in the polarization of the backscattered electromagnetic field. The measured operating frequency (2.46 GHz) of the tag is very close to the resonant frequency of the patch antenna and consequently, the Axial Ratio reaches its highest value. Moreover, the phase difference (see Fig. 6) does not vary with frequency and is very close to 270 • at 2.46 GHz. As expected, the electromagnetic field backscattered by the tag is then righthanded circularly polarized. Fig. 6. Measured axial ratio of the electromagnetic field backscattered by the tag as a function of frequency (solid red) and Phase difference between vertical and horizontal components of this field as a function of frequency (dashed blue). The vertical dashed black line indicates the operating frequency (f 0 = 2.46 GHz). These measurement results are obtained from jumper connections (0 Ω resistances) to the modified CPTL, the "parallel" setup. Fig. 7. Measured axial ratio of the electromagnetic field backscattered by the tag as a function of frequency (solid red) and Phase difference between vertical and horizontal components of this field as a function of frequency (dashed blue). The vertical dashed black line indicates the operating frequency (f 0 = 2.46 GHz). These measurement results are obtained from connecting a resistance R = 20 Ω to the modified CPTL, "series" setup.

B. LHCP-to-LHCP Conversion

We achieve here the CP-to-CP conversion from using a passive impedance load able to affect significantly the backscattered electromagnetic field backscattered by the tag, and to generate left-handed circularly polarized backscattered field. A lumped resistance R = 20 Ω is used in the "series" circuit setup, as illustrated in Fig. 4b.

From Fig. 7, we can observe a narrow-band response (about 2%) in which the required polarization is achieved. At the operating frequency, the Axial Ratio reaches its minimum value (< 1.4 dB). Fig. 7 displays the measured phase difference between vertical and horizontal components of the electromagnetic field backscattered by the tag as a function of frequency. The phase difference is of 83 • (very close to 90 • ) at the operating frequency and consequently, the field backscattered by the tag is left-handed circularly-polarized, as expected.

C. LHCP-to-LP Conversion (-60 • slant)

The third polarization conversion is the CP-to-LP conversion, or a -60 • slanted LP response. In this case, we have two lumped resistances bridging the central conductor to the antenna's ground, in the "parallel" circuit setup. The values of the two resistances are R = 56 Ω.

Fig. 8 displays the measured Axial Ratio of the electromagnetic field backscattered by the tag. It exceeds 40 dB and consequently, ensures a good polarization isolation. The A circular polarization is achieved at frequencies outside the bandwidth of interest, since teh Axial Ratio is lower than 3 dB below 2.22 GHz and above 2.67 GHz. As expected, we observe from Fig. 8 that the measured magnitude of the crosspolar component (30 • slant) reaches its minimum value at the operating frequency (2.46 GHz). From this measurement result, we conclude that the field backscattered by the tag at the operating frequency is purely linearly polarized, and the polarization inclined of -60 • from the original Vertical and Horizontal base.

D. LHCP-to-LP Conversion (9 • slant)

For the final polarization conversion, the impedance load of the tag leads to another LP backscattered electromagnetic field, with a slant angle lower than 9 • . This is implemented using the "series" circuit setup with a lumped resistance equal to R = 120 Ω.

The resulting Axial Ratio of the electromagnetic field backscattered by the tag is found higher than 25 dB, leading to a good isolation, as shown in Fig. 9. Moreover, it can be observed that the cross-polar component (99 • slant) reaches its minimum also at the operating frequency (2.46 GHz). However, the cross-polarized component of the backscattered electromagnetic field is not zero and the polarization is inclined by 9 • from the original Vertical and Horizontal base. Fig. 9. Measured axial ratio of the electromagnetic field backscattered by the tag as a function of frequency (solid red) and magnitudes of orthogonal modes' components of this field as a function of frequency: 9 • slanted copolar (dashed blue) and its cross-polar magnitude (dash-dotted magenta). The vertical dashed black line indicates the operating frequency (f 0 = 2.46 GHz). These measurement results are obtained from connecting a resistance R = 120 Ω to the modified CPTL, "series" setup.

V. CONCLUSION In this study, an impedance loaded patch antenna acting as a passive tag is presented, which can achieve four different polarization of the backscattered electromagnetic field (namely LHCP, RHCP and two slanted LP), when illuminated by a circularly-polarized electromagnetic field. Only four different resistance values are required to control the backscattered field polarization. Experimental results confirm the low axial ratio (less than 1.5 dB) predicted by a backscattering model and full-wave electromagnetic simulations in case of circularlypolarized (RH or LH) backscattered fields, and the excellent isolation (25 dB) in case of (-60 • and 9 • slanted) linearlypolarized backscattered fields. The proposed technique based on polarization conversion from impedance loaded two-port tag may solve propagation issues faced in indoor applications of wireless sensor networks, specially when clutter presents minor levels of depolarization. This solution may be implemented without the need of battery or power supply, when considering passive tags. Moreover, LHCP-to-LHCP conversion can be advantageously applied to mitigate the impact of the electromagnetic clutter in a wireless link and potentially, increase the reader-to-tag separation distance in cluttered environments.

Fig. 1 .

 1 Fig. 1. The two-port microstrip patch antenna operating at 2.45 GHz: (a) front view and (b) side view. Location of the two ports are given by x f and y f , respectively (a = 0.65λ, ly = lx = 0.37λ, x f = y f = 0.09λ, t air = 0.04λ, t subs = 0.007λ and εr = 4.3, where λ = 122.4 mm).

Fig. 2 .

 2 Fig. 2. Measured and simulated scattering parameters S 11 and S 22 at the two input ports 1 and 2 of the microstrip antenna shown in Fig. 1: (a) Magnitude (in dB) and (b) Phase (in degrees).

Fig. 3 .Fig. 4 .

 34 Fig. 3. Measured and simulated co-polar gain at 2.44 GHz in (a) the E-plane and (b) H-plane (dashed blue : MWS CST simulation results; dash-dotted red : measured gain when port 1 is excited and port 2 is loaded by a 50 Ω impedance, and the solid black: the measured gain when port 2 is excited and port 1 is loaded by a 50 Ω impedance.

Fig. 5 .

 5 Fig. 5. Experimental setup in the anechoic chamber with identical horn (Txand Rx-) antennas and the tag (SUT) placed on the plastic hollow disk over a foam support.

Fig. 8 .

 8 Fig.8. Measured axial ratio of the electromagnetic field backscattered by the tag as a function of frequency (solid red) and magnitudes of orthogonal modes' components of this field as a function of frequency: -60 • slanted co-polar (dashed blue) and its cross-polar magnitude (dash-dotted magenta). The vertical dashed black line indicates the operating frequency (f 0 = 2.46 GHz). These measurement results are obtained from connecting resistances equal to 56 Ω to the modified CPTL, the "parallel" setup.

ACKNOWLEDGMENT

The Authors gratefully acknowledge the technical support on the measurements' setup of this work by Ph.D M. Caillet. The authors are also thankful for the insightful discussions with Ph.D S. Bories on backscattering studies.


Nicolas Moreau
email: moreau@lirmm.fr

Michel Leclère
email: leclere@lirmm.fr

Madalina Croitoru
email: croitoru@lirmm.fr

Distinguishing Answers in Conceptual Graph Knowledge Bases

In knowledge bases (KB), the open world assumption and the ability to express variables may lead to an answer redundancy problem. This problem occurs when the returned answers are comparable. In this paper, we define a framework to distinguish amongst answers. Our method is based on adding contextual knowledge extracted from the KB. The construction of such descriptions allows clarification of the notion of redundancy between answers, based not only on the images of the requested pattern but also on the whole KB. We propose a definition for the set of answers to be computed from a query, which ensures both properties of non-redundancy and completeness. While all answers of this set can be distinguished from others with a description, an open question remains concerning what is a good description to return to an end-user. We introduce the notion of smart answer and give an algorithm that computes a set of smart answers based on a vertex neighborhood distance.

Motivation

In the semantic web age, a large number of applications strongly rely on the building and processing of knowledge bases (KB) for different domains (multimedia, information management, semantic portals, e-learning, etc.). The formal languages used for representation will encounter obvious scaling problems and therefore rely on implicit or explicit graph based representations (see for example Topic Maps, RDF, Conceptual Graphs, etc.) As a direct consequence, querying such systems will have to be done through graph based mechanisms and, accordingly, optimization techniques implemented [START_REF] Prud'hommeaux | SPARQL Query Language for RDF[END_REF].

In ICCS'08 [START_REF] Leclère | Query-answering cg knowledge bases[END_REF], we identified the semantic database context in which a set of answers has to be computed. For this case, there are two kinds of answer graphs: answers as subgraphs of the knowledge base graph that are used for browsing the KB or for applying rules; and answers as graphs, independent of the KB, corresponding to the classical use of a querying system 1 . With this latter kind of answer, an important problem concerns detecting redundant answers. Unlike classical databases, redundancies are not limited to duplicate tuples. Indeed, the presence of unspecified entities (generic markers in CG or blank nodes in RDF) and also a type hierarchy leads us to consider that an answer which is more general than another as redundant. In [START_REF] Leclère | Query-answering cg knowledge bases[END_REF], we studied this problem and proposed to return irredundant forms of the most specific answers to a query.

An important problem arising in this context is ultimately related to the nature of a KB vs. a database. With a classical database, one can assume that a query designer knows the database schema and is thus able to build a query corresponding to its needs. With a KB, the schema is extended to an ontology and the different assertions are not supposed to instantiate a specific frame (the knowledge is semi-structured). Consequently, it is difficult for a query designer to specify the content of the searched knowledge: he/she wants to obtain some information about a specific pattern of knowledge. The suppression of redundant answers only by comparing answer graphs independently of the KB results in the problem not being considered. A better way to address the redundancy problem consists of completing the answer graphs with their neighborhood to obtain more detailed answers in order to return some relevant knowledge to the end-user in order to get insight (restitution, reflet) into the diversity of the knowledge in the KB. Moreover, users seem to prefer answers in their context (e.g. paragraph) rather than the exact answer [START_REF] Lin | What makes a good answer? the role of context in question answering[END_REF].

In this paper we focus on answers given in a graph based form. Our motivation stems from the homogeneity of preserving the same format between the KB, query and answer. Moreover, this will allow the reuse of answers as a KB for different future answers (see for example nested queries). Note that while this paper focuses solely on the problem of distinguishing graph based answers, the same research problem will arise and results will be obtained when of answers are represented as a tuple.

Contribution and related work

Figure 1 shows a query, a conceptual graph formalized KB (see section 3.1) and all five answers to the query in the KB (from A 1 to A 5 , in gray in the picture).

The problem that arises in this scenario is how to define relevant answers when they are independent of the KB (i.e. a set of answer graphs and not a set of answer subgraphs of the KB). For instance, answers A 1 and A 5 are equivalent ("there is a human who owns an animal"), and knowledge expressed by these answers is expressed by all of the others. The open world assumption makes it impossible to state that all humans or animals represent distinct elements of the described world. Therefore it seems preferable to only return answers that bring more knowledge, i.e. in our example that "Mary owns a cat" and "a human owns a dog". But another relevant answer could be that "there is a human knowing Mary who owns a cat".

The contribution of the paper is to refine our preceding notion of redundancy between answers, to take the knowledge of the KB into account, through the

Q KB A1 A2 A3 A4 A5 2 1
Animal: * own Human: * notion of a fair extension of an answer, a graph that specifically describes an answer. Thus, an answer is irredundant if there is such a "fair" extension. A special case of this problem (when the answer is a concept node) corresponds to the problem of Generation of Referring Expressions (GRE) studied in the conceptual graph context in [START_REF] Croitoru | A Conceptual Graph approach to the Generation of Referring Expressions[END_REF], that we extend for our purposes. Based on the extended notion of redundancy, we define two answer subset properties of non-redundancy (there is no redundant answer in the subset) and completeness (each answer is redundant to an answer of the subset). We then explain how to compute all the non-redundant and complete subsets of answers, based on a redundancy graph. We then discuss what is a good set of referring graphs to be returned to the user, and give an algorithm that fulfills these good properties.

As previously mentioned, a special case of answer identification was studied in [START_REF] Croitoru | A Conceptual Graph approach to the Generation of Referring Expressions[END_REF]. The RDF query language SPARQL offers a way to describe answers (by the DESCRIBE primitive) but it does not address the specific problem of distinguishing one answer from another according to semantically sound syntactic criteria. The problem of answer redundancy in the Semantic Web context has been studied in [START_REF] Gutierrez | Foundations of semantic web databases[END_REF], but the redundancy stated in this paper concerns the union of all answers, and corresponds, in the CG field, to the classical notion of irredundancy (see section 3.1), as opposed to our redundancy between answers.

In an article about OWL-QL [START_REF] Fikes | OWL-QL, a language for deductive query answering on the Semantic Web[END_REF] the notion of server terseness is defined, which is the ability of a server to always produce a response collection that contains no redundant answers (i.e. there is no answer that subsumes another one). This corresponds to our previous notion of redundancy defined in [START_REF] Leclère | Query-answering cg knowledge bases[END_REF].

In the next section, preliminary notions about conceptual graphs and our query framework are given. Section 4 deals with the extended notion of redundancy between answers and its application to a subset of answers. In section 5 we discuss the relevancy of the set of referring graphs returned to the user. We conclude our work in the last section.

Preliminary notions

Simple Graphs

The conceptual graph formalism we use in this paper has been developed at LIRMM over the last 15 years [START_REF] Chein | Conceptual Graphs: Fundamental Notions[END_REF]. The main difference with respect to the initial general model of Sowa [START_REF] Sowa | Conceptual Structures: Information Processing in Mind and Machine[END_REF] is that only representation primitives allowing graphbased reasoning are accepted.

Simple graphs (SGs) are built upon a support, which is a structure S = (T C , T R , I, σ), where T C is the set of concept types, T R is the set of relations with any arity (arity is the number of arguments of the relation). T C and T R are partially ordered sets. The partial order represents a specialization relation ( t ′ ≤ t is read as "t ′ is a specialization of t"). I is a set of individual markers. The mapping σ assigns a signature to each relation specifying its arity and the maximal type for each of its arguments.

SGs are labeled bipartite graphs denoted

G = (C G , R G , E G , l G )
where C G and R G are the concept and relation node sets respectively, E G is the set of edges and l G is the mapping that labels nodes and edges. Concept nodes are labeled by a couple (t : m), where t is a concept type and m is a marker. If the node represents an unspecified entity, its marker is the generic marker, denoted * , and the node is called a generic node, otherwise its marker is an element of I, and the node is called an individual node. Relation nodes are labeled by a relation r and, if n is the arity of r, it is incidental to n totally ordered edges.

A specialization/generalization relation corresponding to a deduction notion is defined over SGs and can be easily characterized by a graph homomorphism called projection. When there is a projection π from G to H, H is considered to be more specialized than G, denoted H ≤ G. More specifically, a projection π from G to H is a mapping from C G to C H and from R G to R H , which preserves edges (if there is an edge numbered i between r and c in G then there is an edge numbered i between π(r) and π(c) in H) and may specialize labels (by observing type orders and allowing substitution of a generic marker by an individual one).

In the following, we use the notion of bicolored SG that was first introduced in [START_REF] Baget | The SG family: Extensions of simple conceptual graphs[END_REF]. A bicolored SG is an SG H = H 0 , H 1 in which a color on {0, 1} is assigned to each node of H, in such a way that the subgraph generated by 0colored nodes, denoted H 0 and called the core of H, is a subSG. H 1 , which is the sub-SG defined by 1-colored vertices and 0-colored concepts that are in relation with at least one 1-colored concept, is called the description.

Query framework

The chosen context is a base composed of assertions of entity existences and relations over these entities, called facts, and stored in a single graph (not necessarily connected) named the knowledge base. This graph is assumed to be normalized if it does not contain two individual nodes with the same marker i. A normal form is easily computed by merging duplicate individual nodes of the graph. On the other hand, we do not require the KB graph to be in irredundant form: a graph G is in irredundant form iff there is no a projection from G in one of these strict subgraphs; otherwise this graph is said to be in redundant form. Indeed, computation of the irredundant form of a graph is expensive as the base can be large [START_REF] Mugnier | On generalization/specialization for conceptual graphs[END_REF] and, moreover, there is not any local criterion for computation of the irredundant form and thus no incremental method (started at each updating of the base) can be expected. Such a KB graph B is simply queried by specifying a SG Q called the query. There is no constraint on the query (normalization or irredundancy). The answers to the query are found by computing the set Π(Q, B) of projections from Q to B. The primary notion of answer consists of returning the set of subgraphs of B image of Q by a projection in Π(Q, B).

Definition 1 (Answer set). The set of answers of a query Q in a base B, denoted Q(B), is {π(Q) | π ∈ Π(Q, B)} 2 .
The first research question we address in this paper is whether this set of answers contains redundant answers? In fact, three kinds of redundancies can arise:

1. Duplication: two answers are identical. There is a duplication when two projections define the same subgraph. This problem can be solved easily by only keeping one of the duplicate subgraphs (this is done in the answer set Q(B)). An example of duplication is given in fig. 3(b) taken as the KB and fig. 3(c) taken as the query: there are two projections from the query whose images are the whole KB.

2.

Inclusion: An answer is contained in another one. There is an inclusion when an answer is in a redundant form. Then its subgraph, in irredundant form, is also an answer. In the previous example (fig. 3(b) and 3(c)), there are two projections that define included answers.

3.

Redundancy: An answer is more general or equivalent than another one.

There is a redundancy when two answers are comparable (thus the knowledge expressed by one is also expressed by another); as an example answers A 1 and A 2 of figure 1.

Inclusion will be studied in section 4.4. The true redundancy problem becomes crucial since the answers are no longer KB subgraphs. Indeed, two answers can appear redundant when they are not really redundant. In [START_REF] Leclère | Query-answering cg knowledge bases[END_REF], we define the notion of redundancy based only on the comparability of the answer graphs. This approach was motivated by the following argument: as the returned set of answers is independent of the KB, the subset of the more specific irredundant answers, denoted R min , is sufficient to bring the entire range of answers. Moreover, R min is minimal in terms of vertex number. In the following section, we characterize the true redundancy.

Dealing with true redundancy

In [START_REF] Leclère | Query-answering cg knowledge bases[END_REF], the completeness criterion (the knowledge expressed by each initial answer is expressed by one of the answers contained in the returned subset of answers) ensures that no knowledge is lost when a redundant answer is deleted. But this redundancy is based only on the comparability of answer subgraphs (that are semantically close as they are specializations of the query).

The true redundancy

The true redundancy has to take the knowledge brought by the neighbor vertices of the answer into account. With this aim, we introduced the notion of extended answer, which is an answer supplemented with some knowledge extracted from its neighborhood.

Definition 2 (Extension of an answer). Let B be a KB graph and Q a query graph. An extension of an answer

A from Q(B) is a bicolored graph E = E 0 , E 1
, where E 0 is isomorphic to A and such that there is a projection π from E to B with π(E 0 ) = A. With the previous definition of redundancy (section 3.2), if two answers have two incomparable extensions, they are two distinct answers and thus have to be considered as non-redundant answers, the one w.r.t. the other one. However, these two answers must not be distinguished in an "artificial" way: i.e. if the answers are distinguished by selectively adding knowledge to the extension of only certain answers but not to all of those which possess this knowledge in their neighborhood.

Definition 3 (Fairness property). An extension E of an answer

A from a set Q(B) is fair iff there is no extension E ′ of another answer A ′ from Q(B) such that there is a projection π from E to E ′ with π(E 0 ) = E ′ 0 and π(E 1 ) = E ′ 1 .
The extension of figure 2 ). An answer A from a set of answers Q(B) is truly redundant if there is no fair extension of this answer.

In the example of fig. 1, answer A 1 is redundant. The search for a fair extension may seem to be a difficult task, considering that the number of extensions that can be generated for an answer is infinite. However, these extensions are semantically bounded by a more specific one that corresponds to an isomorphic copy of the base, A, B \ A 3 . Naturally, the more one adds knowledge to the extension (the more it is specific), the more one potentially distinguishes this answer. So A is irredundant only if A, B \ A is a fair extension.

Theorem 1. There is a fair extension E of an answer A iff A, B \ A is a fair extension.

Proof. By contraposition. Suppose that there is a fair extension E = E 0 , E 1 of A and that A, B \ A is not a fair extension of A. A, B \ A is an extension of A and is isomorphic (without considering the colors) to B. As E is an extension of A, there is a projection

π from E to B such that π(E 0 ) = A. As A, B \ A is not a fair extension of A, there is a projection π ′ from A, B \ A to B such that π(R 0 ) = A. So there is a projection π ′′ = π • π ′ from E to B such that π ′′ (E 0 ) = A. Thus E is not a fair extension of A. ⊓ ⊔ Corollary 1. An answer A of Q(B) is truly irredundant iff A, B \ A is a fair extension.

The GRE problem

The problem of finding a fair extension of an answer is strongly related to the problem of generation of referring expressions (GRE) known in the natural language processing field, which aims to describe an object in a scene such that the description only refers to this object. The GRE problem was formalized in the CG framework in [START_REF] Croitoru | A Conceptual Graph approach to the Generation of Referring Expressions[END_REF], where the scene is an SG and the object to identify is a concept of the SG. A referring graph of a concept v is a subgraph of the KB containing this concept, and a distinguishing graph is a referring graph whose v is a fixed point for all projections of the graph in the KB. Our problem of answer redundancy can be seen as an extension of this formalization.

Definition 5 (Referring graph).

A referring graph of a subgraph G ′ of a graph G is a subgraph R of G that contains G ′ as a subgraph. To distinguish G ′ from the rest of the referring graph, we denote it as a bicolored graph

R = R 0 , R 1 where R 0 = G ′ and R 1 = R \ G ′ . Definition 6 (Distinguishing graph). A referring graph R of a subgraph G ′ of a graph G is distinguishing if, for each projection π from R to G, π(R 0 ) = G ′ .
The referring graph of figure 2(b) is a distinguishing graph of the answer A 2 of figure 1, contrary of the referring graph of figure 2(a). We can now link the true redundancy notion with the existence of a distinguishing graph for a given answer. The next properties strengthen the notion of true redundancy by showing its independence in the query and thus in the other answers.

Property 1. Let A be an answer of Q(B).

There is a fair extension of A iff there is a distinguishing graph of A w.r.t. B.

Proof. Let E = E 0 , E 1 be a fair extension of A. Then π(E) is a distinguishing graph of A w.r.t. B. On the other hand, a distinguishing graph of A is also a fair extension of A.

⊓ ⊔

Corollary 2. An answer A of Q(B) is irredundant iff R = A, B \ A is a distinguishing graph of A w.r.t. to B.
Thus, determining whether an answer is irredundant can be done by testing the distinguishness of the referring graph built from KB. However, the cost of such a test is exponential in the size of the KB.

Redundancy and subset of answers

Since the redundancy of an answer has been defined, it could be considered that for building a set of answers without redundancies one could simply remove redundant answers. However, the redundancy defined in the preceding section hides the fact that they are two types of redundancy. This is shown in fig. 3

(a query and three different KBs) :

The first case will arise when an answer is completely redundant with respect to another answer (fig. 3(b)). This means that A 2 is redundant w.r.t. A 1 but the reverse does not hold. In this case, we say that A 2 is strongly redundant w.r.t. A 1 . Thus, we only return the answer A 1 .

The second case arises when there are a set of answers which are redundant amongst themselves (fig. 3(c) and 3(d)). In these two examples, an answer is redundant with respect to the others and vice-versa. In this case, we say that the answers are mutually redundant and we have to choose an answer in this set.

Note that the answer redundancy problem still holds in KBs in irredundant forms, as in the example of fig. 3(d). ). An answer A is redundant to an answer A ′ iff for each referring graph R A of A, there is a projection

π from R A to a referring graph R A ′ of A ′ with π(R A 0 ) = π(R A ′ 0 ) = A ′ .
One can test the redundancy relation with the KB referring graph:

Property 2. An answer A is redundant to an answer A ′ iff there is a projection

π from A, B \ A to a referring graph R A ′ of A ′ with π(A) = A ′ .
Therefore an answer A is redundant to an answer A ′ , the redundancy relation between A ′ and A defines the two previously seen redundancy cases:

Definition 8 (Redundancies between answers). Given A and

A ′ ∈ Q(B), such that A is redundant to A ′ : -A is strongly redundant to A ′ if A ′ is not redundant to A ; -A and A ′ are mutually redundant if A ′ is redundant to A ;
Based on the notion of true redundancy, we can refine our notions of nonredundancy and completeness of subsets of answers that we defined in [START_REF] Leclère | Query-answering cg knowledge bases[END_REF] : Definition 9 (Non-redundant subset of answers). A subset of answers A of Q(B) is non-redundant if there are no two answers A and A ′ ∈ A such that A = A ′ and A is redundant to A ′ .

Definition 10 (Completeness). A subset of answers

A of Q(B) is complete if for each answer A of Q(B) there is an answer A ′ of A such that A is redundant to A ′ .
We define a graph of redundancies based on the notions of strong and mutual redundancies. All types of redundancies of definition 8 can be viewed as relations on Q(B) 2 , for example (A, A ′ ) belongs to the strong redundancy relation if A is strongly redundant to A ′ . Thus we can characterize properties of these relations. Particularly, mutual redundancy defines equivalent classes over the set of answers, and strong redundancy links all answers of an equivalent class to all answers of another equivalent class. We construct the redundancy graph such that each vertex is an equivalent class, and is linked by the strong redundancy:

Definition 11 (Graph of redundancy). The graph of redundancy G = (V, E) of Q(B) is a directed graph, where vertices represent equivalent classes of the mutual redundancy relation and where there is an edge between v 1 and v 2 if all answers of the class represented by v 1 are strongly redundant to all answers of the class represented by v 2 . To construct a complete and non-redundant set of answers, one has to only choose a single answer per equivalent class (to avoid mutual redundancy), only from equivalent classes that are sinks (to avoid strong redundancy), and for all of them (to be complete). This is why there is more than one non-redundant complete subset in the second example (fig. 4(b)): there is an equivalent class that is a sink and contains more than one element ({A 5 , A 6 }). Theorem 2. A subset of answers A of Q(B) is complete and non-redundant iff for each sink in the redundancy graph there is a single answer of A that is represented by this sink.

Proof. Given a non-redundant and complete subset of answers A. Non-redundancy means that there is a single answer for each equivalent class represented in A and that there are no two answers A i and A j such that there is a path from A i to A j . Completeness ensures that for all answers A i of Q(B) (particularly answers belonging to a sink) there is an answer A j such that A i is redundant to A j . So A has to contain an answer of each sink. When combining completeness and non-redundancy, only one answer of each sink is taken.

• Given a subset of answers A that is composed of an element of each sink of the redundancy graph. Given two answers of A. These answers are not mutually redundant because there are no two answers of the same equivalent class. These answers are not strongly redundant because each answer comes from a sink. Thus A is non-redundant. For each answer A i of Q(B), either there is an answer A j of the same equivalent class in A (thus A j is redundant to A i ), or there is an answer A k in A that comes from a sink such that there is a path from the equivalent class of A i to the sink, and thus A i is redundant to A k . A is complete.

The construction of a redundancy graph combines the problem of finding all projections of a graph into another graph (to compute the set of answers) and the problem of computation of the irredundant form of a graph. Indeed, as stated by property 2, computation of all redundancy links of all answers used to construct the graph is based on all projections of the most specific referring graph of each answer (i.e. a bicolored isomorphic copy of the whole KB). Therefore, a way to compute all redundancy links is to compute all projections from the KB into itself, and check images of a each answer by all projections.

Inclusion of answers

As mentioned in section 3.2, the inclusion of answers is one of the problems that can occur. If treated as a kind of duplication, included answers are just deleted from the answer set before computation of a non-redundant complete subset. But this approach is not the best one. We think that the inclusion problem should be treated after the redundancy problem.

In the example of fig. 5, there are seven answers: three that contain only one relation (A 1 , A 2 , A 3 ), three that contain two relations (A 12 4 , A 13 , A 23 ), and one with three relations (A 123 ). Considering all answers, only answers A 2 , A 3 and A 23 are irredundant (see fig. 5(c)), but it is not suitable to keep A 2 and A 3 .

Otherwise, if only non-included answers are kept, this leads to keeping answers that were redundant to deleted answers (here A 123 , redundant to A 23 ), which is not good. So the best way is to deal with redundancy first (by computing a subset that is non-redundant and complete) and to delete included answers after that. In the previous example, this strategy led to the subset {A 23 }.

Redundancy at a considered distance

In the query framework section, it was stated that computation of the irredundant form of the KB is a difficult problem. But we also see that computation of the redundancy graph also requires finding all projections of the KB into itself. Thus, we propose to restrict referring graphs of an answer to a portion of the base that is "near" this answer. This is also due to the fact that a referring graph that contains too much knowledge, even if it distinguishes an answer, does not help the user much. So we propose to bound referring graphs by a distance k, and to only consider vertices that are in the distance field of one of the vertex of an answer, which forms the k-neighborhood graph of the answer: Definition 12 (k-neighborhood graph). Given a KB B, a subgraph S of B, and a step k (k ≥ 0), the k-neighborhood graph, denoted N k (S), is defined recursively by:

-N 0 (S) = S -N n+1 (S) is composed of N n (S) expanded by every relation r not in N n (S)
and which is linked to a concept of N n (S), and by all concepts linked to r.

Recursion stops when n = k or N n (S) = N n+1 (S) and returns N n (S).

It seems obvious that all definitions put forward previously should now take this constraint into account. Bounding referring graphs can be seen as a restriction of the KB, which is now considered as the union of the k-neighborhood graph of each answer, for a given distance.

Definition 13 (Truncated KB). Given a KB B, a query Q, and a distance k ≥ 0, the truncated KB at distance k is B k = A∈Q(B) N k (A) Now we can apply all previous definitions to the truncated KB. For example, an answer

A of Q(B) is irredundant considering the distance k iff R = A, B k \A is a distinguishing graph of A w.r.t. B k (see corollary 2).

Building smart answers

In the previous section, redundancy and completeness were only studied from a theoretical standpoint. A more user-aspect oriented standpoint was introduced in the section 4.5. Even if the user gets a subset of answers that is non-redundant and complete, he/she has no way to distinguish answers, i.e. the only assumption that can be made is that there is, for each answer, a way to distinguish them from the others. Otherwise, property 1 states that the most specific referring graph is one of them, but it usually contains too much knowledge.

So what are the properties of a really good set of referring graphs returned to the user? To keep the notions of non-redundancy and completeness, only answers of such a subset of answers should have a referring graph. As all of these answers can be distinguished, all referring graphs should be a distinguishing graph. Finally, to not introduce unnecessary redundancies in the set of referring graphs, there should be only one distinguishing graph by referred answer. A set of referring graphs that fulfills these properties is called a set of smart answers: Definition 14 (Set of smart answers). A set of smart answers S of a query Q on a KB B is a set of distinguishing graphs of all answers of a non-redundant complete set A of Q(B) such as |S| = |A|.

We propose the Bounded Smart Answers (BSA) algorithm (see algo. 1) that takes the answers and a distance as parameters, and returns a set of smart answers of truncated KB at distance k such that each extension is the minimal k-neighborhood graph that distinguishes the answer5 . Theorem 3. Algorithm BSA(Q(B), k) produces a set of smart answers of Q on the truncated KB B k .

Proof. In DAK, all referring graphs are constructed with the same distance. Therefore, thanks to the distance conservation property of the projection, that if there is a bicolored projection from N k (A i ) to N k (A j ), there is a projection from N k (A i ) to B k such that image of the core of N k (A i ) is equal to A j (i.e. N k (A i ) is a referring graph of A j in B k ). For each answer A that belongs to an equivalent class that is not a sink, A will not be returned by DAK because of the second "foreach" of DAK. The third foreach of DAK ensures that for each equivalent class that is a sink, the algorithm will only add one (the first taken) answer that belongs to this class once the good distance is reached. Thus

Conclusion

We extended our previously defined notion of answer redundancy. Our new framework now considers answers but also descriptions (called referring graphs) that can distinguish an answer amongst others. These descriptions could be adapted to query languages of the semantic web, e.g. by giving a formal definition of the SPARQL DESCRIBE query form. Therefore this new redundancy is now linked to the whole KB. Based on this new redundancy, we refined two other previous definitions concerning subsets of answers: non-redundancy property (there is no redundant answer in the subset) and completeness (each answer is redundant to an answer of the subset). We proposed a way to construct all non-redundant and complete subsets of answers using a redundancy graph. We introduced the notion of smart answer and gave an algorithm that computes a set of smart answers based on a vertex neighborhood distance.

Answer redundancy arises because of open world assumption and undefined objects (generic concepts). A deeper redundancy still exists, that is not related to the formalized world (the KB), but rather to the "real world" (described by the KB). For example, it is possible that non-redundant answers "a big cat" and "a white cat" refer to a single cat of the "real world", which is big and white. The study of this new kind of redundancy can provide a foundation for using aggregation operators (e.g. number of results to a query) in graph based KB query languages.

Fig. 1 .

 1 Fig. 1. Query, KB and highlighted answers.

Fig. 2 .

 2 Fig. 2. Several extensions of answer A2 of fig. 1.

Fig. 2

 2 Fig. 2 represents several extensions of answer A 2 of fig. 1. Note that the extensions are not necessarily isomorphic copies of subgraphs of the KB.With the previous definition of redundancy (section 3.2), if two answers have two incomparable extensions, they are two distinct answers and thus have to be considered as non-redundant answers, the one w.r.t. the other one. However, these two answers must not be distinguished in an "artificial" way: i.e. if the answers are distinguished by selectively adding knowledge to the extension of only certain answers but not to all of those which possess this knowledge in their neighborhood.

  (b) is a fair extension of the answer A 2 of figure 1, contrary to the extension of figure 2(a). One can now give a definition of the true redundancy: Definition 4 (True redundancy

Fig. 3 .

 3 Fig. 3. Different cases of redundant answers

Fig. 4 (

 4 Fig. 4(a) represents the redundancy graph of query and KB of fig. 1, whereas fig. 4(b) represents the redundancy graph of query of fig. 3(a) and KB defined by the union of KBs of fig. 3(b), 3(c) and 3(d).

Fig. 4 .

 4 Redundancy graph of the previous examples.

Fig. 5 .

 5 Fig.5. A query and a KB that produce included answers, and their redundancy graph.

Data:

  Answers Q(B), a distance k Result: A set of smart answers of truncated KB B k begin i ← 0 D ← ∅ // distinguished answers S ← ∅ // smart answers while i ≤ k or D = Q(B) do D ′ ← DISTING AT K(Q(B), D, i) D ← D ∪ D ′ foreach A ∈ D ′ do S ← S ∪ { A, N i (A) \ A } return S end Algorithm 1: BOUNDED SMART ANSWERS (BSA)the union of all answers returned by DAK is a non-redundant complete subset of answers of B k . As BSA returns only one graph per answer of the computed non-redundant complete subset, BSA returns a set of smart answers of B k . ⊓ ⊔

For example, in SPARQL, as blank node labels can be renamed in results, see[START_REF] Prud'hommeaux | SPARQL Query Language for RDF[END_REF] ¶

2.4.

"Answer set", denoted Q(B), and "answer" notions correspond respectively in our previous work[START_REF] Leclère | Query-answering cg knowledge bases[END_REF] to notions of "answers by image subgraphs", denoted RIP (Q, B), and "images of proof". Names have been changed for simplification.

For clarity, we sometimes denote subgraphs of KB as cores or descriptions of bicolored graph instead of their isomorphic copies.

Answer Aij represents the answer that is the union of answers Ai and Aj.

Note that comparisons in DAK (algo. 2) are between bicolored graphs, that is B ≤ B ′ iff there is a π from B ′ to B such that π(B ′ 0 ) = B0.

Algorithm 2: DISTING AT K (DAK)


Nicolas Charles

Johann Tuduri

Dominique Guyonnet

Jérémie Melleton

Olivier Pourret

Rare Earth Elements in Europe and Greenland: A geological potential? An overview

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