Lorenza Della Donna

Maurizio Ronci

Paolo Sacchetta

Carmine Di Ilio

Bartolomeo Biolatti

Giorgio Federici

Carlo Nebbia

Professor Andrea Urbani
email: andrea.urbani@uniroma2.it

Della Donna

Lorenza Della Donna

Carmine Di Ilio

A food

Keywords: Biomarker, Food safety, Growth promoting agents, Mass spectrometry, Proteomics

According to the 2005 residue monitoring plans, in the European Union Member States the number of noncompliant PEAs, such as, sexual steroids, β-agonists, and corticosteroids, is reported to be less than 0.3% of the examined samples. However, the results from the histological investigations performed in target organs and analyses of seized black market preparations suggest that the chemical manipulation of cattle growth is still a matter of concern [START_REF] De Brabander | Presence and metabolism of the anabolic steroid boldenone in various animal species: A review[END_REF]. The remarkable discrepancy between the reported official data and the real situation may be due to the ever changing strategies for animal illegal treatment. For example, these would involve: (i) the "week-end schedule," consisting of administration of rapidly metabolized active principles on Fridays, (ii) the use of hormone precursors, (iii) the use of a combination of different active principles at very low dosages, (iv) the use of principles of unknown chemical structure or not included in the national residue monitoring plans [START_REF] Courtheyn | Recent developments in the use and abuse of growth promoters[END_REF]. Any of these procedures can result in the generation of (false) negative data. This is especially true when samples are screened for the presence of PEA residues with immunochemical assays, often characterized by a quite low sensitivity. There is therefore the urgent need to develop biological assays able to ascertain exposure of food producing animals to a wide number of illegally administrated PEAs [START_REF] Kuiper | Illegal use of beta-adrenergic agonists: European Community[END_REF]. Proteomics represents a powerful tool to detect the modifications of protein expression resulting from the exposure of living animals to such agents, which are known to act at molecular level by altering the rate of gene transcription. A previous study from our laboratory already proved the usefulness of the proteomic approach in detecting biomarkers of illicit treatments [START_REF] Gardini | Proteomic investigation in the detection of the illicit treatment of calves with growth-promoting agents[END_REF]. However, we are still facing the lack of proteomics investigations in biological samples collected from living animals. Among body fluids, serum may constitute a potential sample for the detection of illegal treatments. Recently, serum has gained an increasing interest in proteomic research for F o r P e e r R e v i e w 4 molecular biomarker discovery, especially for human clinical issues, where it is considered potentially the most easily accessible sample specimen for biomarker elucidation [START_REF] Ebert | Advances, challenges, and limitations in serum-proteome-based cancer diagnosis[END_REF][START_REF] Villanueva | Correcting common errors in identifying cancer-specific serum peptide signatures[END_REF][START_REF] Matharoo-Ball | Serum biomarker profiling in cancer studies: A question of standardisation?[END_REF].

To date, a limited number of proteomic studies on bovine tissues and biological fluids have been published [START_REF] Wilkins | Progress with proteome projects: Why all proteins expressed by a genome should be identified and how to do it[END_REF][START_REF] D'ambrosio | Comparative proteomic analysis of mammalian animal tissues and body fluids: Bovine proteome database[END_REF][START_REF] Ardekani | Clinical potential of proteomics in the diagnosis of ovarian cancer[END_REF][START_REF] Sanchez | Inside SWISS-2DPAGE database[END_REF][START_REF] Sanchez | The mouse SWISS-2D PAGE database: A tool for proteomics study of diabetes and obesity[END_REF][START_REF] Kaji | Protein database of Caenorhabditis elegans[END_REF][START_REF] Wait | Strategies for proteomics with incompletely characterized genomes: The proteome of Bos taurus serum[END_REF][START_REF] Talamo | Proteins from bovine tissues and biological fluids: Defining a reference electrophoresis map for liver, kidney, muscle, plasma and red blood cells[END_REF].

The aim of this study was to develop and characterize a MALDI time-of-flight MS (MALDI-TOF-MS) proteome profile of the bovine serum in order to provide a suitable biotechnological framework for on field investigations of food safety. In particular, focusing on the low molecular proteome profile ranging between 3 and 20 kDa, we developed a biomarker detection strategy to highlight exposure of food producing species to illegal drugs and PEAs. The achieved classification models have been benchmarked on the discrimination of calves undergoing treatment with different PEA protocols currently employed on bovine illicit treatment.

Methods

Animal treatments and source of serum samples

Serum samples were obtained from 4-to 6-month-old crossbred male veal calves subjected to different experimental treatments or from animals (n = 17) reared in a breeding farm and officially declared untreated (C UT ). In all cases, blood samples were collected by venipuncture in Falcon vessels, allowed to clot and centrifuged at room temperature for 10 min at 2000 rpm (814 × g). The resulting sera were stored at -80°C in 1.5 mL aliquots until further use.

Twenty-four calves were randomly allotted to four groups of six individuals each. One group consisted in untreated animals (C 2 ); the other groups were subjected to one of the following administrations at increasing dose rates (150-200 mg i.m. per capita) at weekly intervals;

(iii) glyburide 2.5 mg + androsterone 1 mg (GLY-AND) per capita per day for 37 days.

Blood samples were collected 24 h after the last treatment.

Serum preparation for MALDI-TOF-MS analysis

An amount of 10 µL of crude equine myoglobin (5 pmol/µL) was added to 10 µL crude sera samples as internal standard (IS). Samples were then desalted, concentrated, and spotted on MALDI-TOF ground steel plate using different solid phase extraction (SPE) procedures.

ZipTips C 4 and C 18 (tip size P10; Millipore, USA) were activated and equilibrated using 50% ACN/H 2 O and 0.1% TFA, respectively. The proteins were let bound to the resin, desalted by washing with 0.1% TFA and eluted directly on a plate together with 2 µL of sinapinic acid satured solution in 30% ACN/0.1% TFA. Strong cationic exchanger ZipTips (SCX) were activated and washed with 0.1% TFA, charged with the sample and eluted on a plate with

MALDI-TOF-MS analysis

All sera samples were analyzed using a MALDI-TOF mass spectrometer. Spectra acquisitions were performed on a Reflex IV and on an UltraFlex III TOF/TOF (Bruker-Daltonics, Germany) MALDI-TOF mass spectrometer instruments equipped with nitrogen laser (λ = 337 nm) and SmartBeam laser, respectively, both working in positive linear mode.

The acquisition range was set to 3-20 kDa; laser power and total number of shots were adjusted for each acquisition to obtain no more than 10 3 ion counts per shot train and between 2 × 10 4 and 3 × 10 4 total ion counts for the base peak. External calibrations were performed using singly and doubly charged β-hemoglobin chain (at 15 868 and 7934.5 Th, respectively), and singly and doubly charged α-hemoglobin chain (at 15 127 and 7564 Th, respectively) from human blood. Heights of MS peaks were normalized to the peak intensity of the equine myoglobin (IS). Spectra were smoothed before analysis. All spectra processing for the validation step was performed using FlexAnalysis 2.0 software (Bruker-Daltonics) with an S/N threshold of 10 and a centroid evaluation of the peaks.

Serum fractionation

An amount of 50 µL of a pool of sera from untreated animals was diluted 1:1 with 0.1% TFA and processed in HPLC using an Agilent 1100 series Liquid Chromatograph (Agilent Technologies, USA) equipped with a reverse phase semiprep-column (C18 HYPERSIL ODS 5 µm, 25 mm i.d. × 200 mm 0.4) and a multidiode array detector monitoring at 280 nm. The flow rate was maintained at 3.8 mL/min and a stepwise gradient from 95% solvent A (0.1% TFA in water) to 95% solvent B (0.1% TFA in acetonitrile) was used. Fractions were

LC-ESI-MS/MS analysis

LC-MS/MS analysis was carried out on a Q-TOF Ultima (Waters, USA) equipped with a nano-Lock-Spray ion source and coupled with a CapLC chromatography system (Waters). A volume of 6 µL of digested fractions was injected and first concentrated on a Trap Column (Waters Symmetry300 C 18 5 µm OPTI-PAK) at high flow rate, then, eluted on a C 18 column (LCPackings DIONEX PepMap 5 µm, 100 Å 75 mm i.d. 250 mm) with a H 2 O/ACN gradient in the presence of 0.2% of formic acid using a precolumn splitter at 200 nL/min. On-line recalibration was performed by constantly infusing a GFP solution at 250 fmol/µL in H 2 O/ACN 0.1% formic acid. The voltage applied to the capillary and the desolvation gas flow rate were tuned up before each analysis to obtain a stable spray. Argon was used as collision gas. The collision energy was automatically chosen from control software as a function of the precursor ion mass. MS/MS spectra were acquired by automatic switching between MS and MS/MS mode. Acquired MS/MS data were converted in a centroid format by ProteinLinx 2.0 software (Waters).

Multivariate data analysis

Collected spectra from experiment 2 and from the independent control set were divided in two groups: belonging to the first group (untreated animals) were C 2 and C UT ; belonging to the second group were 17βE, 17βT, or GLY + AND. Spectra were processed in order to extract a consistent data matrix of masses and intensities by means of the MatLab routine LIMPIC [START_REF] Mantini | LIMPIC: A computational method for the separation of protein MALDI-TOF-MS signals from noise[END_REF]. To execute the multivariate data analysis, this matrix was exported to Simca-P+ (Umetrics, Sweden). All data were scaled to unit variance and centered in the preprocessing step. Principal components analysis (PCA) was run on the complete dataset.

For projection to latent structure partial least square-discriminant analysis (PLS-DA), two independent datasets were generated by selecting even and odd observations in the original dataset: all even observations were included in the training set used for the generation of model and all odd observations were integrated in the prediction set used to validate the model itself. We initially addressed the development of a robust proteomics platform in order to explore biomarker discovery investigations in bovine sera. We chose to implement linear MALDI-TOF-MS molecular profiling coupled with protein SPE to obtain reproducible and appropriate sized datasets, in order to possibly classify calves subjected to illicit treatments.

Results

Extraction strategy

We selected Sinapinic Acid as MALDI matrix given the high ionization properties on intact proteins [START_REF] Urbani | Properties of the detergent solubilised cytochrome c oxidase (cytochrome cbb(3)) purified from Pseudomonas stutzeri[END_REF].

We tested different type of SPE strategies on packed pipette tips (ZipTip) encompassing reverse phase materials such as C 4 and C 18 [START_REF] Biroccio | Differential posttranslational modifications of transthyretin in Alzheimer's disease: A study of the cerebral spinal fluid[END_REF], cationic exchange (SCX) and metal affinity (MC) resins to find the best performing strategy in terms of unique MS signals and repeatability. Figure 1 shows the average spectrum (n = 6) for each type of extraction applied to officially declared untreated control samples (C UT Section 2&blcok;Please check the change made█). Table 1 reports ((Fig. 1)) ((Table 1))

Considering the number of distinct signals peaks, their distribution over a wide m/z range (3-20 kDa) and the reproducibility in extracting the IS for ZipTip C 4 SPE, this method was selected to develop our MALDI-TOF-MS sera profiling platform. The C 4 SPE method allowed us to reproducibly profile 79 signals, which resulted in a typical MALDI-TOF mass spectrum of bovine serum proteins. In order to identify the main molecular features of this profile, we used an LC-MALDI-TOF-MS fractionation approach coupled with an nLC-Q-TOF-MS/MS protein identification strategy. Figure 2 shows the separation profile of the semipreparative chromatographic run and the resulting MALDI-TOF-MS spectra for "nonempty" fractions. The analysis of the collected fractions by Q-TOF-MS/MS gave rise to 28 identified proteins (Table 2). Some of them were attributed to fragments of higher molecular weight proteins while others match, in the investigated mass range, with tentative multiple charge species of large proteins. Nevertheless, few identified proteins from the Q-TOF-MS/MS experiments did not correlate with any of the reported MALDI-TOF-MS signals. Such behavior might have different explanations: it can be due to the limited mass range explored in LC-MALDI-MS fractionation experiments (which, however, is super-imposable with the expected C 18 HPLC column retention [START_REF] Wang | Effects of chromatography conditions on intact protein separations for top-down proteomics[END_REF]), to nonpredictable post-translational modifications, or to fragmentation of proteins.

Protein signals identification

((Fig. 2)) ((Table 2))

Analytical performances

Reproducibility is a key aspect of using MALDI-TOF-MS as a semiquantitative analytical instrument. Variability could arise from sample handling, sample preparation, and mass spectrometric platform. We followed the guideline for full analytical validation imposed by several international organizations, including FDA. 3).

((Table 3))

The relative ratio of the representative endogenous peaks versus the ISs has been investigated in order to evaluate the repeatability of the method. Table 4 is reported the MALDI intra-and interday repeatability, showing a variability lower than 15% (n = 18) for intraday series and lower than 16% (n = 18) for interday series.

((Table 4))

All the acquisitions for the figure of merit referring to the analytical validation study have been performed on the Reflex IV instrument. Nevertheless we found similar or better performances on the Ultraflex series; therefore, this latest instrument has been used for the study of groups.

Application to PEA's illicit treatment

To evaluate a direct application of bovine sera proteins profiling, we focused our interest on biomarker identification for PEA's illicit treatment. To this end, serum samples were used, including samples from controls (C 2 ) and treated groups (17βE, 17βT, or GLY + AND). nonparametric statistic (Fig. 3, Box and Whisker plots are reported at the side of each signal) was used to evaluate the significance of the differences between the classes after signal intensities normalization, based on the added IS (heart horse myoglobin 16 952.3 Th). This type of normalization flattened the differences observed in the total ion count weighted profile, as shown in Fig. 3e depicting the IS average signal in the different groups. Due to both the low number of observations and their non-normal distribution inside the groups, a Mann-Whitney test for independent samples was chosen in order to assess the statistical significance of differences. A more appropriate test, when more than two groups must be compared, is the Kruskal-Wallis one way analysis of variance on ranks. The results of both statistical tests are very similar. Resulting p values for the differences between groups at 95% of confidence are shown in Table 5. This direct comparison highlighted four signals that specifically discriminate the control calves from those belonging to the different treatments (6950, 7451, 8733, and 14 900 Th; Fig. 3). Signal at 6950 Th was significantly higher for each treatment group and it was assigned to the sushi domain 3-4 of the β 2 -glycoprotein-I (β 2 GPI, apolipoprotein H, NCBI#: P17690), by combining the described LC-MALDI-TOF-MS fractioning with nLC-MS/MS protein identification (Table 2). Signals at 7451 and 14 900 Th resulted significantly different from the ones highlighted in the untreated animals only for two out of three groups (i.e., 17βT and GLY + AND); signal at 8733 Th was found significantly different only for the 17βT treated group. To calculate an ROC curve based on the normalized intensity of the signal of sushi 3-4 of β 2 GP-I, the number of control samples was increased by adding to C 2 (n = 6) a set of 17 sera samples collected from a homogeneous group of veal calves reared in the same farm, formally considered as untreated animals (C UT ).

All treated animals were assigned to the same class. The ROC curve for the signal at 6950 Th demonstrated high sensitivity and specificity (Fig. 4). In particular, adopting the optimal selection criterion ((Figs. 3,4)) ((Table 5))

Despite the statistical significance of single signals differences, a better interpretation of such a large dataset could be provided by a multivariate approach. In order to combine the overall MS molecular sera profile, we have applied a multivariate analysis using both PCA and PLS-DA. All data were scaled to unit variance and the PCA performed on all samples resulted in a nine principal components (PCs) model with an explained variance of 76.1% (Table 6). Two strong outliers were present in the overall cohort of 65 data points; nevertheless the distribution of residues was indicative of a homogeneous dataset. The first component explains the 22.4% of the variance; on the x-axis three distinct areas are visible (Fig. 5a), suggesting a partial unsupervised clustering of the samples. Even if a separation between control and treated calves is visible in the PCA model, no significant clustering was obtained between the different growth promoting agents treatments.

((Fig. 5))

((Table 6)) replicates of investigated samples (Fig. 5b). The built mathematical model had a predictive power of 69.4% (Table 7). The loading plot (Fig. 5c) highlights the strong statistical weight of sushi 3-4 fragment of the β 2 GP-I, which is the first variable in the "importance of variables in the projection" (VIP) plot (Fig. 5e); in effect the signal of the β 2 GP-I at 6950 Th resulted absent in all control from the validation group (C UT ). The other signals, resulted significantly different in the univariate analysis (7451, 8733, and 14 900 Th), but apparently did not show a very high influence upon the combined class clustering for all the growth promoting agents treatments.

((Table 7))

The crossvalidation of the PLS-DA model was obtained by classifying the prediction dataset (Fig. 5d). The samples were distributed in two different clusters, both in the region of the control samples and in the area of PEA's treated calves. The region of the plane in which sera from untreated calves are clustered is highlighted. By considering the prediction made by this model, it can be noted that 3 out of 17 treated samples resulted misclassified (false negatives), while only 1 out of 13 control samples was misclassified (false positive). Our study focuses on the low range proteome repertoire of sera in the peptide and proteins range detectable between 3 and 20 kDa. This specific range represents a serum fraction of great biological relevance since it encodes information on protein and peptides, proteolytic maturation, and post-translational modifications [START_REF] Yi | Inhibition of intrinsic proteolytic activities moderates preanalytical variability and instability of human plasma[END_REF][START_REF] Tammen | Peptidomic analysis of human blood specimens: Comparison between plasma specimens and serum by differential peptide display[END_REF]. The high analytical performances achieved with a MALDI-TOF-MS platform in this mass window allow a fine microcharacterization of molecular species. The study of the low molecular range was also suggested by the intent to investigate proteins in a range not detectable from other common proteomic techniques, such as 2-DE and SDS-PAGE. Moreover, the electrophoretic approach followed by MS analysis is laborious and time-consuming, and in SDS-PAGE the signal often results spurious, since a given zone could be an envelope of bands with closely spaced mass molecular values.

Discussion

The choice of employing serum rather than plasma (EDTA or citrate), as suggested by HUPO, was driven by the absolute requirement to have an easy collectable sample in any farms. In particular, plasma collection was not pursued as it would require special care in avoiding erythrocyte hemolysis, which might return massive hemoglobin signal contamination in the MALDI-TOF-MS profile.

Despite the criticism and setbacks [START_REF] Baggerly | Signal in noise: Evaluating reported reproducibility of serum proteomic tests for ovarian cancer[END_REF][START_REF] Diamandis | Analysis of serum proteomic patterns for early cancer diagnosis: Drawing attention to potential problems[END_REF][START_REF] Ransohoff | Lessons from controversy: Ovarian cancer screening and serum proteomics[END_REF][START_REF]Guidance for Industry, Bioanalytical Method Validation[END_REF], MALDI-TOF technique has the potential for enormous impact on the field of biomarker discovery as it can offer a high-throughput analysis method applicable to complex biological mixtures. The analytical performances open platform MS profiling approach is different from the traditionally accepted analytical measurement. In fact, critical parameters like LOD, LOQ, precision, or linearity have to be carefully evaluated when considering pure quantitative methods on specific and well-defined molecules but they become senseless in a semiquantitative analysis especially when dealing with biological macromolecules in complex mixtures and no information on target molecular species is available. For this concern, if parameters like resolution, mass accuracy, and repeatability are inside an acceptable range we can consider the method adequate to conduct such a proteomics investigation.

Our results concerning inter-and intraday repeatability confirm CV% lower than the limits for full analytical validation imposed by several international organizations, including FDA [START_REF]Guidance for Industry, Bioanalytical Method Validation[END_REF]. The high mass resolution (FWHM>1000) and accuracy (∼100 ppm) allows to clearly identify specific protein products characteristic of calf sera. The overall evaluation of these analytical features plainly demonstrates how a fine tuned proteomic platform, based on MALDI-TOF-MS, can be employed for semiquantitative molecular biomarker investigations.

The number and the quality of proteomic approaches aimed to investigate biological fluids and tissues is constantly increasing but to keep pace with the rapid development of new unknown substances used for growth promotion still urges the development of screening and confirmatory methods. These methods must be suitable to deal with the relatively large numbers of samples and to guarantee high reliability of results.

In our work, we undertook an initial annotation effort in order to set a reference molecular framework for further biomarker investigations. A number of reference MALDI-TOF-MS Multivariate PLS-DA analysis also confirmed the high discriminatory load of this molecular species. Nevertheless, the separation in two large classes of treated and untreated animals accomplished with the PLS-DA analysis result in a predictive power of only 69.4%, as explained by Q 2 Y value, which is the measure of how well the model predicts new data. Such a lower discrimination power might be due to the characteristic of multivariate approaches since they might be influenced by every slight change in the data profile. A biological sample-to-sample variation was expected considering how intrinsic differences due to genotypic and phenotypic characteristic, health condition, etc. could influence the overall protein profile and, consequently, the serum low range proteome.

The three protein signals associated to a specific type of PEAs treatment in the univariate analysis, did not find confirmation by global PLS-DA. Given the sample number required to consolidate a multivariate data analysis we could not apply this procedure to single class treatments. The importance of the fragment of β 2 GP-I in the construction of the model can be noted in the loading plot (Fig. 5c).

In order to detect illegal treatments, the most convenient criterion is the one that gives 100% sensitivity, thus excluding false negative cases, while doubtful cases undergo further analysis by classical toxicological confirmation methods. Our results highlight the role of sushi 3-4 fragment of the β 2 GP-I (apolipoprotein H) as a potential reproducible marker of PEAs treatment. The ROC curve for this signal demonstrates high sensitivity and specificity: choosing 100% sensitivity results in 74.4% specificity.

The bovine β 2 GP-I is a plasma glycoprotein, identical to the human counterpart for the 81% of the sequence and circulating as a free protein or associated to lipoproteins. Although quite a lot is known about the structure of β 2 GP-I, its biological function is still unclear. It is known that β 2 GP-I can bind to negatively charged substances, such as DNA, heparin and negatively charged phospholipids in vivo [START_REF] Kochl | Novel interaction of Apolipoprotein (a) with Beta 2 glycoprotein I mediated by the Kringle IV domain[END_REF], but the meaning of such interaction remains to It is also known that β 2 GP-I may serve as a major factor in clearing the plasma liposome [START_REF] Chonn | Beta 2 glycoprotein I is a major protein associated with very rapidly cleared liposomes in vivo, suggesting a significant role in the immune clearance of "nonself" particles[END_REF] as well as an anticoagulant in blood [START_REF] Brighton | Beta 2-glycoprotein I in thrombosis: Evidence for a role as a natural anticoagulant[END_REF]. The lipid-binding and transportation functions are considered as a basic mechanism related to its physiological and pathogenic functions. Its first isolation from the bovine serum, dating back to the 1990s, was due to its strong inhibiting effect in the incorporation of thymidine into fetal calf erythroid cells [START_REF] Li | Isolation from fetal bovine serum of an apolipoprotein-H-like protein which inhibits thymidine incorporation in fetal calf erythroid cells[END_REF].

More recently, its presence as a low abundant protein was highlighted in colustrum, suggesting an eventual special physiologic relevance to the health and development of calves in lactation [START_REF] Yamada | Identification of lowabundance proteins of bovine colostral and mature milk using two-dimensional electrophoresis followed by microsequencing and mass spectrometry[END_REF]. However, apart from his anticoagulant action, its role, as well as the one of the human form, is still uncertain. Due to the recent increase in the use of anabolic steroids among athletes, the modulation of the apolipoproteins upon administration of anabolic steroids has already been established [32].

The interpretation of the observed increase in serum β 2 GP-I expression in calves from all experimentally treated groups is difficult and goes beyond the scopes of our study.

Interestingly, another truncated form of a bovine apolipoprotein Apo-A1, was detected in plasma samples from calves experimentally administered a combination of boldenone and boldione, two androgenic sexual steroids [33]. Taken together, all these data suggest a linkage between administration of anabolic steroids and/or hormones and apolipoprotein expression. However, more investigations should still be conducted to understand the underlying mechanism and the actual existence of a direct link.

The possibility to export such platform to a territory monitoring plan and to extend this approach to other food safety issues, such as dioxin food contamination, can be considered Although further research is warranted to corroborate the data obtained in the present study, serum proteomics seems to be a promising technology to enhance the food safety controls in living animals.

F

  resulting edible products is extremely worrying for health risk of consumers.

  i) 17β-estradiol (17βE), six i.m. administrations at increasing dose rates (20-40 mg i.m. per capita) at weekly intervals; (ii) 17β-testosterone (17βT), six i.m.

2

  µL of 5% ammonium hydroxide in H 2 O/MeOH 70:30. After air drying, 1 µL of sinapinic acid saturated solution in 30% ACN/0.1% TFA was added to the samples. Metal chelating surface ZipTips (MC) were equilibrated with 0.1% acetic acid in H 2 O/ACN 50:50, charged with 200 mM FeCl 3 in 10 mM HCl, washed with Milli-Q grade water and washed again with 1% acetic acid in H 2 O/ACN 80:20. Next, they were equilibrated with 0.1% acetic acid in H 2 O/ACN 90:10, charged with the sample and eluted in a clean vial with 2 µL of 0.3 M ammonium hydroxide. An amount of 1 µL of the eluted solution was spotted on the plate, allowed to partially dry and overlaid with 1 µL of sinapinic acid saturated solution in 30% ACN/0.1% TFA.

  30 s intervals (1.9 mL) and concentrated by vacuum centrifugation to approximately 150 µL. Concentrated fractions were analyzed by linear MALDI-TOF-MS and subsequently used for protein identification by nLC-Q-TOF-MS/MS after reduction, alkylation, and digestion with DTT 100 mM, iodoacetamide 200 mM, and trypsin 0.5 µg/µL, respectively.

  -Daltonics) was used for differential peaks selection between the following groups: C 2 , 17βE, 17βT, and GLY + AND; Box and Whisker graphs and Mann-Whitney tests were carried out by means of MedCalc 9. Kruskal-Wallis one way analysis of variance on ranks was performed with SigmaStat version 3.5 with the Dunn's method.

  the number of corresponding signals and SD for the same set of samples. The average number of peaks with S/N>10 for C 4 extraction is 79 with a SD 5.8 and with uniform distribution of signals over the investigated mass range. C 18 showed an unbalanced extraction capacity resulting in a few MS signals in the high mass range and high abundance in the low mass range. SCX and MC were clearly not suitable for our purpose since they gave rise to an extremely low number of proteins, mainly identified in a restricted molecular weight interval ranging between 6500 and 9000 Th.

  consolidate the MALDI-TOF-MS bovine serum investigation, we assessed the analytical performances of such a profiling strategy and MS analysis. Mass accuracy of MALDI-TOF mass spectra, after external calibration, resulted in approximately 100 ppm, with resolution (FWHM) higher than 1000. The mass accuracy of the measurements was calculated on six signals chosen between the identified and annotated protein signals. The mass deviation from the calculated average molecular mass for the IS was equal to 0.02 Da, in excellent agreement for MALDI-TOF-MS data in this mass range (Table

  Samples were independently analyzed by MALDI-TOF-MS after C 4 SPE. Each MALDI-TOF mass spectrum showed approximately 80 distinct peaks at S/N>10. Descriptive

  of signal at 6950 for ith sample and IS i I is the internal standard intensity for the same sample, we can achieve 97.7% specificity with 95% confidence limits at 85.4-99.5%, and 97.2% sensitivity with 95% confidence limits at 87.7-99.6% for the classification of groups. The area under the curve is 0.992 and the significance level p is 0.0001.

14 A

 14 more powerful statistical analysis for class discrimination is the PLS-DA, in which group information is specified a priori and helps drive the separation. PLS-DA was carried out on all samples. Observations were divided in a training dataset, employed to construct the model, and a prediction dataset was used to perform a crossvalidation. In order to reach a significant number of observations we kept the treated group as a single cohort: this assumption originated by considering the similar biological effects of the treatments and the results of the unsupervised PCA analysis. The generated PLS-DA model showed five significant components and gave rise to a complete clustering of the two groups for all

  very short breeding cycle, veal calves represent the meat producing bovine category mostly subjected to illicit treatments with PEAs. Their residues can accumulate in meat and offals and potentially affect consumer's health. Body fluids, like serum, represent one of the most convenient samples to collect and investigate; serum characterization is a fundamental milestone to detect functional molecular biomarkers of illicit treatment.

  as required by several international organizations regardless of the instrumental technique applied. In this light, it is necessary to perform a validation study both of the extraction strategies and of the MS technology employed before using any quantitative or semiquantitative platform to pursuit an analytical molecular investigation. Nonetheless any

  been identified by employing HPLC reverse phase fractionation[START_REF] Lopez | High-resolution serum proteomic profiling of Alzheimer disease samples reveals disease-specific, carrier-proteinbound mass signatures[END_REF] on semipreparative set-up. Such a fractionation scale of the intact protein level was conveniently performed with a relatively large quantity of serum. Several linear MALDI-TOF-MS peaks were observed in each fraction and, as expected, more than one peak might correspond to the same gene product. Moreover, considering the lack of complete genome sequence databases, signals annotations might suffer from the poor prediction of all the presumed maturation process and post-translational modifications.Predicting the possible application of serum proteomic signature in the detection of illicit treatments, we compared the low molecular weight serum protein profile, of untreated calved to the one of calves exposed to different compounds. In particular, the protocols used for the treated groups mocked the most commonly used illegal treatment schedules. These include: the most effective natural estrogen (17βE), one of the most active androgens (17βT), and an association of moderately active anabolic agent (AND) and insulin-like sulfanylurea-derived synthetic agent (GLY). The collected data have been processed both by classical univariate statistical approach and by the more powerful multivariate approach. The latter is considered a valuable tool to discriminate among different classes and predict the behavior of new observations. We highlighted one putative protein fragment significantly different from the comparison of sera between treated and untreated animals. The normalized intensity of the signal at 6950 Th resulted significantly higher for every treatment group, thus, validating the relationship among altered metabolic pathways and serum MS profile. The signal corresponding to the β 2 GP-I, at 6950 Th, was not found in any of the samples from 4-monthold calves declared "untreated" by the farmer (C UT ). In fact, the sampled animals did not show overt clinical signs of treatment, like abnormal muscle hypertrophy, nervousness, polypnea, or increased heart frequency.

  one main goal of this state-of-the-art study in the development of Proteomics functional biomarker. The high throughput features of the proposed MALDI-TOF-MS analysis combined to a well defined and simplified classification model provide a powerful tool for the detection of PEAs usage.

  a step forward to the detection of biomarkers of illicit treatment in veal calves serum in the low molecular weight range (3-20 kDa) through a postgenomic approach.

Figure 3 . 25 Figure 4 .

 3254 Figure 3. Superimposed average spectra from control (red line) and treated groups (green,

Figure 5 .

 5 Figure 5. (a) PCA on all samples return a nine PCs model with an explained variance of

  Draisci, R., Montesissa, C., Santamaria, B., D'Ambrosio, C. et al., Integrated analytical approach in veal calves administered the anabolic androgenic steroids boldenone and boldione: Urine and plasma kinetic profile and changes in plasma protein expression.

		24
	[32] Hartgens, F., Kuipers, H., Effects of androgenic-anabolic steroids in athletes. Sports
	Med. 2004, 34, 513-554.
	[33] Proteomics 2007, 7, 3184-3193.
	o r F o r F o r Figure 1. Average MALDI-TOF spectra of bovine sera samples after different types of F ZipTip extraction. (a) C 4 ; (b) C 18 ; (c) SCX; (d) MC. As expected, ZipTip C 18 was best suited o r to extract a high number of species in the low mass range whereas ZipTip C 4 resulted in a
	P P P P more homogeneous extraction profile. SCX and MC were clearly inappropriate for our
	e e e e purpose. IS signal (heart horse myoglobin) was clearly detectable only in C 4 ZipTip
	spectrum.	e r e r e r r e
	R e v i e R e v i e R e v i e R Figure 2. Average spectrum with identified signals and corresponding gel/stack view of not-e empty collected fractions. Numbered signals in the spectrum correspond to the proteins v i e identified by LC-MS/MS experiments in Table 2.
		w w w w

Table 1 .

 1 Average number of signals extracted by each ZipTip type (S/N>10)

	ZipTip	Sample	Sample	Sample	Sample	Sample	Sample	Average	SD
	type	1	2	3	4	5	6
	C 4	81	90	76	76	79	74	79.3	5.8
	C 18	59	77	80	58	79	106	76.5	17.5
	MC	11	4	8	7	6	8	7.3	2.3
	SCX	6	5	7	8	6	9	6.8	1.5

Table 2 .

 2 List of identified proteins by nano-LC-nano-ESI-Q-TOF-MS/MS fragmentation

	experiments
	N	Proteins	Mass value	Expected mass of	Mass of un
	o.		(Th)	fragments (Da)	precurso
	1	Apolipoprotein C-II short form	7945.0	7944.9	860
	2	Apolipoprotein C-III	8218.7	8217.0	10 6
	3	Apolipoprotein A-II short form 1-76	8566.4	8566.6	11 2
	4	β-2-Microglobulin	11 635.6	11 635.2	13 6
	5	Hemoglobin subunit alpha	15 055.0	15 053.2	15 0
	6	Transthyretin	13 559.0	13 557.3	15 7
	7	Hemoglobin subunit beta	15 957.0	15 954.4	15 9
	8	Complement component 3 res38-113	8776.8	8777.1	17 0
	9 1	α-1-Acid glycoprotein Coagulation factor XIII A1 subunit [M + 2H + ]	n.a. 11 369.6	21 253.0 22 744.5	21 7 22 7
	1 1	Hypothetical protein Vl1a protein Apolipoprotein A-I [M + 2H + ]	n.a. 13 775.5	-27 549.1	24 6 30 2
	1	β-2-Glycoprotein 1 (Apolipoprotein H) sushi 3-4	6949.0	6949.0	38 2
	1	α-2-HS-glycoprotein	n.a.	13 253.7-12 531.5	38 4
	1	Hypothetical protein Apolipoprotein A-IV	n.a.	41 032.2	43 0
	1	Pigment epithelium-derived factor precursor	n.a.	44 056.3	46 3
	1	α-1-Antiproteinase	n.a.	43 693.9	46 4
	1	Endopin 2C	n.a.	-	46 8
	1	Glial fibrillary acidic protein, Coil 1B	11 835.0	11 832.1	49 4
	2	LOC507464 protein (Fragment)	n.a.	-	51 1
	2	Antithrombin-III	n.a.	-	52 3
	2	α-1-B glycoprotein	n.a.	-	53 5
	2	Fibrinogen alpha chain	n.a.	-	67 0
	2	Kininogen-1, cystatin 2, cystatin 3	n.a.	13 876.5-13 285.2	68 8
	2	Coagulation factor II	n.a.	-	70 4
	2	Serotransferrin (transferrin) (siderophilin)	n.a.	-	77 7
	2	Complement factor H sushi 6 sushi 11sushi 15	6995.0	6997.8	140
			6737.0	6737.8
	7 2	Complement C3 C3a anaphylatoxin	7651.0 8931.0	7647.5 8933.2	187
	n.a., not assigned.

Table 3 .

 3 Comparison of SD and mass error in ppm (n = 20) for homologous peaks in different samples for the acquisitions on the Reflex IV and Ultraflex III mass spectrometers Average mass of IS (heart horse myoglobin theoretical mass = 16 952.3).α and β hemoglobin singly and double charged were used to perform quadratic calibration of TOF. Additional internal calibration was performed on the mass of IS.

		Average mass	RSD (Th)	Mass error (ppm)
		(Th)
	Reflex IV	7945.2	1.25	158

█Please explain the significances of italic and asterisk used in the table█Table 4 .

 4 Inter-and intraday repeatability

					28
	13 677	1380.93	147.33	10.67
	13 735	444.84	67.08	15.08
	13 765	567.07	84.59	14.92
	17 159	61.16	8.46	13.82
	Repeatability interday (n = 18)
	Twelve signals present in at least 75% of
	samples were chosen to evaluate repeatability. F Average, SD and RSD were calculated on the o r normalized intensity for each signal.
			P
				e
	m/z	Intensity	SD	RSD e r
	Repeatability intraday (n = 18)	R e
	6 820 6 839	180.13 249.08	18.85 33.51	10.46 13.45	v i e
	6 883	116.81	18.06	15.46	w
	12 634	323.67	51.00	15.76
	12 792	215.31	31.68	14.71
	13 413	241.54	36.12	14.96
	13 558	7117.17	1094.73	15.38
	13 639	1142.42	158.29	13.86

Table 5 .

 5 p-Values for Kruskal-Wallis one way analysis of variance on ranks

		C 2 versus	C 2 versus	C 2 versus
	m/z
		GLY + AND	17βE	17βT
	6950	<0.05	<0.05	<0.05

Table 6 .

 6 PCA-X; observations (N) = 58; Variables (K) = 85 (X = 85, Y = 0)The PCA model returned nine significative PCs. The rate of the total variance explained by each PC is reported in the R 2 X column; the cumulative value is reported in the R 2 X(cum) column. The total explained variance of the model is 76.1%.

	Page 29 of 35		Biotechnology Journal
	PC	Fraction of sum of squares (SS) of	Fraction of the total variation of Y's
		the entire X's explained by the	that can be predicted by the current
		current component	component
		R 2 X	R 2 X(cum)	Q 2	Q 2 (cum)
	1	0.224	0.224	0.117	0.117
	2	0.151	0.374	0.0119	0.127
	3	0.103	0.478	-0.0314	0.0998
	4	0.0709	0.548	-0.0246	0.0776
	5	0.0612	0.61	0.0565	0.13
	6	0.0505	0.66	-0.0303	0.103
	7	0.038	0.698	-0.0306	0.0759
	8	0.0341	0.732	-0.0149	0.0622
	9	0.0283	0.761	-0.0487	0.0165
				Wiley-VCH

Table 7 .

 7 PLS-DA; observations (N) = 30; variables (K) = 87 (X = 85, Y = 2) Fraction of SS of the entire X's explained by the current component Fraction of SS of all the Y'sThe PLS-DA model returned five significative PCs. The cumulative predictive power is reported for each PC in the Q 2 (cum) column. The mathematical model has a total predictive power of 69.4%.

		Fraction of the total varia
	explained by the current	of Y's that can be predic
	component	by the current compone

Wiley-VCH Biotechnology Journal

We are grateful to Dr. Luisa Pieroni for her critical discussion and corrections. This work was supported by the Piemonte Regional Grant CIPE "Identification of molecular biomarkers of illicit treatment on calves by proteomics and genomic investigations."

The authors have declared no conflict of interest.

((Funded by: Piemonte Regional Grant CIP))


Alessandro E P Villa

Igor V Tetko

Cross-frequency coupling in mesiotemporal EEG recordings of epileptic patients

Keywords: Mesiotemporal lobe epilepsy, epileptic focus, cortico-cortical resonances, bispectrum, bicoherence

Cross-frequency coupling in mesiotemporal EEG

recordings of epileptic patients.

Introduction

Patients with medically refractory mesiotemporal epilepsy are characterized by an actively discharging epileptiform region that induces paroxysmal behavior in a homologous site of the contralateral hemisphere [START_REF] Williamson | Characteristics of medial temporal lobe epilepsy: Ii. interictal and ictal scalp electroencephalography, neuropsychological testing, neuroimaging, surgical results and pathology[END_REF][START_REF] Steinhoff | Ictal scalp eeg in temporal lobe epilepsy with unitemporal versus bitemporal interictal epileptiform discharges[END_REF]. Entrainment of both temporal and frequency domain characteristics of temporal lobe activity may depend on both local connections and external inputs, mainly corticocortical and thalamic [START_REF] Canolty | High gamma power is phase-locked to theta oscillations in human neocortex[END_REF][START_REF] Jensen | Cross-frequency coupling between neuronal oscillations[END_REF]. The exact localization and spreading pattern of the seizure can be assessed with electrophysiological recordings only from subdural and depth electrodes (King and Spencer, 1995) and is otherwise determined by neuroimaging techniques [START_REF] Velasco | Accuracy of ictal spect in mesial temporal lobe epilepsy with bilateral interictal spikes[END_REF][START_REF] Joo | Unitemporal vs bitemporal hypometabolism in mesial temporal lobe epilepsy[END_REF]. However, the invasiveness and the costs of these methods may not be made available or tolerated by several patients.

Non-invasive electroencephalographic (EEG) recordings with scalp electrodes are routinely performed on epileptic patients but these data may be distorted by skull defects and underlying lesions or deformities of the brain [START_REF] Scherg | Multiple source analysis of interictal spikes: goals, requirements, and clinical value[END_REF]. Semi-invasive (foramen ovale, Fov) electrodes allow to record electrical activity in the vicinty of the inferior mesial temporal region with less artifacts [START_REF] Wieser | The 'foramen ovale electrode': a new recording method for the preoperative evaluation of patients suffering from mesio-basal temporal epilepsy[END_REF][START_REF] Carter | Cost-efficient localization of seizures of mesiotemporal onset with foramen-ovale electrodes[END_REF] and become more often used in addition to the standard international EEG 10/20 montage positions. Then, these recordings may offer the advantage of exploring mesiotemporal lobe activity with higher-order frequency domain analysesbispectral analysis-that allow to determine the nonlinear com-Email addresses: Alessandro.Villa@ujf-grenoble.fr (Alessandro E.P. Villa) ponents of the interactions in the frequency domain [START_REF] Brillinger | An introduction to polyspectra[END_REF][START_REF] Lii | Cross-bispectrum computation and variance estimation[END_REF][START_REF] Schanze | Phase correlation among rhythms present at different frequencies: spectral methods, application to microelectrode recordings from visual cortex and functional implications[END_REF].

Bicoherence is a normalization method which compares the actual bispectrum with a zero phase bispectrum, i.e. a bispectrum with the highest degree of phase coupling [START_REF] Nikias | Bispectrum estimation: a digital signal processing framework[END_REF]. It shows the degree of phase coupling between frequency components of one or more signals. In brain electric activity, such non-linearities would occur when two frequency components are in harmonic resonnance or if two brain electric waves interact and generate a new energy component at a frequency, called Quadratic Phase coupling, which is the sum of the frequencies of its source components. Bispectral analysis was used for the study of non-linear interactions in several animal studies [START_REF] Villa | Corticofugal modulation of functional connectivity within the auditory thalamus of rat[END_REF][START_REF] Villa | Non-linear corticocortical interactions modulated by cholinergic afferences from the rat basal forebrain[END_REF]. In human studies, bispectral analysis of EEG [START_REF] Ning | Nonlinear analysis of the hippocampal subfields of ca1 and the dentate gyrus[END_REF][START_REF] Sigl | An introduction to bispectral analysis for the electroencephalogram[END_REF][START_REF] Johansen | Development and clinical application of electroencephalographic bispectrum monitoring[END_REF] became routinely applied for studying the levels of arousals and anesthesia with controversial outcome [START_REF] Hagihira | Changes of electroencephalographic bicoherence during isoflurane anesthesia combined with epidural anesthesia[END_REF][START_REF] Miller | Does bispectral analysis of the electroencephalogram add anything but complexity?[END_REF][START_REF] Schulz | Bispectral index monitoring does not improve anesthesia performance in patients with movement disorders undergoing deep brain stimulating electrode implantation[END_REF] and to cognitive studies of areal interactions [START_REF] Freeman | Aperiodic phase re-setting in scalp eeg of beta-gamma oscillations by state transitions at alpha-theta rates[END_REF][START_REF] Jensen | Cross-frequency coupling between neuronal oscillations[END_REF]. Dynamic brain oscillations have extensively been studied in epileptic patients and revealed several changes in the power spectra of EEG signal before and after the epileptic seizures [START_REF] Van Quyen | Analysis of dynamic brain oscillations: methodological advances[END_REF]. Recent evidence of spectral instabilities during the pre-ictal intervals [START_REF] Aksenova | Detection of spectral instability in eeg recordings during the preictal period[END_REF] suggest that scalp and Fov recordings might reveal more information about the activity of neural circuits after careful analysis of bispectra. In the current study we define a novel index, called index of resonance, based on third order spectral (bispectral) analysis of EEG recordings. We report the application of this method to EEG data (scalp and Fov record-ings) recorded in patients characterized by medically refractory complex partial seizures. In addition to its clinical application, such index might be used in other studies to describe dynamic changes of neural interactions.

Methods

Patients data

We analyzed the data of ten patients, 9 men and 1 woman (mean age, 26.6 years; range, 13-39 years), all with therapy refractory mesiotemporal epilepsy. Four patients were affected by mesotemporal sclerosis and underwent hippocampal amygdalectomy. Five were affected by different types of tumors and underwent resection of the tumor. One patient was characterized by a traumatic lesion of the temporal lobe and underwent a 2/3 anterior temporal lobe resection. All patients were seizurefree during at least one year post-operation. The patients were consecutively examined in the local program for presurgical evaluation, which has been approved by the ethical committee of the University of Bern. Informed consent about using the routine diagnostic data for research purposes was given by all patients prior to entering the presurgical evaluation program.

EEG data acquisition

For scalp EEGs the standard 10/20 montage positions were used with referential montages to two preauricular electrodes. For analyzing scalp EEG, the 18 signals from electrodes Fp1, F3, F7, F9, T3, T5, P3, C3, O1 from the left side and Fp2, F4, F6, F8, T4, T6, P4, C4, O2 from the right side were used. Fov EEG was recorded with 2 foramen ovale electrodes [START_REF] Wieser | The 'foramen ovale electrode': a new recording method for the preoperative evaluation of patients suffering from mesio-basal temporal epilepsy[END_REF], each having four contacts, manufacturing type CAD-FO-B4 (Ad-Tech Medical Instrument Corp., Wisconsin). We used an EEG-1032 amplifier system (La-Mont Medical, Inc., Wisconsin). After passing an anti-aliasing filter with a cutoff frequency of 70 Hz and an attenuation of 24 dB/oct. The EEG signals were sampled at 200 Hz and A/D conversion had a resolution of 16 bit. We used the Harmonie 5.0 software (Stellate Systems, Montreal) for EEG data acquisition. The onset of the seizure was determined by the first clinical manifestation (in the majority of the cases an epigastric aura) reported by the patient or observed by a person familiar with the recognition of mesio-temporal lobe epileptic seizure. Electroencephalo-graphically, seizure onset was defined as the first unequivocal appearance of typical continuous epileptiform activity recognized by an experienced electroencephalographer like spikes, polyspikes, spike and wave patterns, evolving and spreading low-amplitude fast or highamplitude slow EEG rhythms, which preceded, accompanied or followed clinical signs. Short (< 2s) bursts of epileptiform EEG potentials without any symptoms or behavioral signs were not interpreted as seizures. The complete EEG recordings were visually inspected and analyzed to make sure that no seizures were missed.

We analyzed 23 EEG samples lasting 20 minutes, including at least 5 minutes pre-ictal and 5 minutes post-ictal. The samples were divided into epochs of 5 seconds.

channel #1 1 k N y(t) = ! ( a(t) + b(t) + a(t) b(t) ) N a(t) = cos(2" 1 t + # a ) b(t) = cos(2" 2 t + # b ) ... ... channel #2 z(t) = ! ( c(t) + d(t) + c(t) b(t) ) N c(t) = cos(2" 1 t + # c ) d(t) = cos(2" 2 t + # d ) b(t) = cos(2" 2 t + # b ) ... ... 1 k N # a , # b , # c , # d are independent phases in [0 , 2"] Recorded signals = 1 1 + 2 2 channel #1 P y ( ) Frequency channel #2 Frequency P z ( ) 1 1 + 2 2 Power spectrum ? P zz ( ) = | z( )| 2 Fourier transform > Z( ) = ! z(t) e -i t 2" N P yy ( ) = | Y( )| 2 Y( ) = ! y(t) e -i t 2" N

Data analysis

Signal analysis functions are subdivided into classes derived from their relationship with the statistical moments and cumulant series. Second order cumulant class includes correlation, power spectrum density and coherence. As second order cumulant statistics decompose the signal into a linear combination of mutually uncorrelated frequency components [START_REF] Huber | Statistical methods for investigating phase relations in stationary stochastic processes[END_REF], they can be applied only to stationary signals and cannot be used to detect signal components which are in non-linear, phase dependent, relationships [START_REF] Nikias | Bispectrum estimation: a digital signal processing framework[END_REF]. Third order cumulant statistics are based on skewness. They can detect whether the signal deviates from normality, i.e. is non-Gaussian [START_REF] Brillinger | An introduction to polyspectra[END_REF][START_REF] Huber | Statistical methods for investigating phase relations in stationary stochastic processes[END_REF][START_REF] Nikias | Bispectrum estimation: a digital signal processing framework[END_REF]. Third order cumulant analysis include the bicorrelation, the bispectrum and the bicoherence. They keep the phase relationship between the signal components and thus can detect if some of them are non linearly coupled.

Third order cumulant analysis of the electrophysiological recordings can be briefly described as follows. Firstly, let us consider a case study where an analog signal from a single channel, e.g. an EEG signal x(t), is recorded during N epochs of equal duration, such that

x(t) = N (a(t) + b(t) + a(t)b(t)) where a(t) = cos(2π f 1 t + ω a ), b(t) = cos(2π f 2 t + ω b ) and f 1 , f 2 represent
two frequencies of periodic processes and ω a ,ω b are phases randomly changed, i.e. uniformly distributed in [0, 2π], for each epoch. Notice the non-linear interaction is represented by the term a(t)b(t) (Fig. 1). The spectral representation of this signal X( f ) is obtained by the Fourier transform

X( f ) = N x(t)e -it2π f . The power spectrum is P xx ( f ) = |X( f )| 2
and its shape will show peaks corresponding to frequencies f 1 , f 2 and f 3 = f 1 + f 2 (Fig. 1).

Power spectrum analysis is unable to differentiate phase relatioships in recorded signals because this analysis is not sufficient to determine if the peak at frequency f 3 corresponds to a genuine non-linear interaction produced by the two oscillatory processes that interact-and generate a third component or if it corresponds to an independent frequency. In order to resolve this ambiguity we compute the bispectrum B xxx , defined by

B xxx = N X( f 1 ) X( f 2 ) , X * ( f 1 + f 2 )
where X * ( f ) is the conjugate of X( f ). B xxx will be near 0 in case of independence [START_REF] Brillinger | An introduction to polyspectra[END_REF], and for the peaks in the bispectrum we estimate the value of the interaction by the bicoherence C xxx , defined by

C xxx = |B xxx | 2 /P xx ( f 1 ) P xx ( f 2 ) P xx ( f 1 + f 2 ).
Let us assume a case study x(t) characterized by an interaction, represented by the term a(t)b(t), between f 1 and f 2 so that a significant value of the bicoherence is observed for bifrequencies ( f 1 , f 2 ). We tested the hypothesis that the bispectrum was equal to zero [START_REF] Huber | Statistical methods for investigating phase relations in stationary stochastic processes[END_REF][START_REF] Brillinger | An investigation of the second-and higher-prder spectra of music[END_REF] at the 99% confidence limit to detect the significant interactions at couples of frequencies f 1 and f 2 . Phase-coupled frequencies f 3 = f 1 + f 2 were determined for corresponding significant bispectral analysis at couples of frequencies f 1 and f 2 . Frequency f 3 defined the "frequency of resonnance". In order to avoid biased sampling (i.e., due to differences in gain of amplitude set for the recording from different subjects) only ten most significant peaks in bicoherence were considered here in each EEG sample.

Results

The bispectral analysis was performed for all channels separatedly in accordance to the side where the epileptogenic focus was located, in a retrospective manner after pathology was determined by magnetic resonance imagery and complementary clinical analyses. The data recorded from the four leads of one foramen ovale electrode were grouped together. We defined an index of resonance IR as the ratio between the relative frequency of peaks in the gamma-band (40-55 Hz) and the relative frequency of peaks in the beta-band (15-30 Hz). This means a large value of IR corresponds to a shift of f 3 towards higher frequencies (gamma-band) and a low value of IR corresponds to a shift of f 3 towards lower frequencies (beta-band).

Table 1 shows the values of IR before, during and after seizure sorted according to the ipsilateral and contralateral hemisphere to the epileptogenic focus. The general pattern was a decrease of IR during seizures (ictal periods) within and across patients in both hemispheres. Notice that in most locations the values of IR after seizure recovered values close to those measured in the pre-ictal period. There are two important exceptions to the general pattern of IR changes. At first, frontal leads F3 / F4 show only a moderate, if any, decrease of IR in the ipsilateral hemisphere but a significant increase (Chi-square test, 2p < 0.001) of gamma-band components in the contralateral hemisphere during the ictal periods. In the latter case the value of IR after seizure tended to recover the pre-ictal level at a slower pace with respect to most locations. Secondly, central leads C3 / C4 in the ipsilateral hemisphere show also a tendency to an increase in IR but the significance level was barely close to 5%. In the contralateral hemisphere the pattern of IR variation for central leads C3 / C4 was in line with the general observation, i.e. a decrease of IR during seizure followed by a recovery close to pre-ictal levels.

The foramen ovale electrodes were located in the vicinity of the mesiotemporal lobe and the subsequent analysis is focused on results obtained from recordings of Fov EEG. Figure 2 il- 3: Scatterplot of the Index of Resonnance (IR) before (PRE), during and after (POST) seizures for nine patients sorted out according to the hemisphere of the epileptic focus and to the etiology of the epilepsy. Mean values ± SEM are indicated. Notice that after seizures the IR tended to be larger in patients affected by mesiotemporal sclerosis vs. tumor for both ipsi-and contra-lateral hemispheres.

lustrates the cumulated distribution of relative frequencies of phase coupling in the range 5 -70 Hz for all patients grouped together and for both hemispheres. We observed a decrease of gamma activity, in particular the disappearance of any frequency of resonnance higher than 55 Hz, and an increase in beta activity during the ictal periods. For both hemispheres grouped together IR was minimal (0.59 ± 0.08, average ± SEM) during seizure and maximal after seizure (1.67 ± 0.18).

The post-seizure period was the most important for the observation of a significant difference (Chi-square test, 2p < 0.05) between IR calculated in the ipsilateral hemisphere to the epileptogenic area (IR = 1.43) vs. contralateral hemisphere (IR = 1.95) This difference was significant for the grouped values and consistently observed for all subjects. During the post-seizure interval IR tended to be larger than during the pre-ictal period. However, in this comparison we observed a greater variability between patients and the comparison of the grouped values sorted by hemisphere was not statistically different.

A more refined analysis was attempted to investigate whether post-seizure IR could differentiate the patients following the etiology of the epilepsy. Two groups were formed with respect to the pathology determined after magnetic resonance imaging, as mesial temporal sclerosis (n=4) or tumor (n=5). After seizure IR was lower in the group of patients with a tumor, in the ipsias well contra-lateral side to the epileptogenic area (Fig. 3) but this tendency was not statistically significant.

Discussion

This study has demonstrated that non-linear analysis of Fov recordings by mean of bispectral analyses provides useful statistical value in localizing the side of the epileptogenic focus in patients who have medically intractable temporal lobe epilepsy. Bispectral analysis allowed us to detect significant changes in Fov EEG that could not be observed by second order cumulants. Our results support the hypothesis that cross-frequency coupling [START_REF] Jensen | Cross-frequency coupling between neuronal oscillations[END_REF], and not merely the power of neural activity, is varied according to changes triggered by the circuits involved in the initiation of the epileptic seizures [START_REF] Van Quyen | Analysis of dynamic brain oscillations: methodological advances[END_REF]. Notice that we computed a single value of IR in each period because we looked for features that could be found in common for several patients. The value of IR could be calculated on shorter time scales (e.g. on a one-minute time base) for a detailed analysis of the evolving seizure and more complex indexes combining time varying IR with spectral instabilities [START_REF] Aksenova | Detection of spectral instability in eeg recordings during the preictal period[END_REF] might represent a valid tool for further clinical assessment.

The application of bispectral analysis to monitor levels of arousal in routine clinical studies is often reduced to one patented measurement called bispectral index (BIS) provided by commercially available devices (Aspect Medical Systems Inc., Newton, MA). The BIS value [START_REF] Kelley | Monitoring Consciousness Using the Bispectral Index During Anesthesia, 2nd Edition[END_REF] is summing up several features of the EEG and it was advised to monitor the depth of anesthesia [START_REF] Avidan | Anesthesia awareness and the bispectral index[END_REF]. However, the comparison of entropy indices with BIS revealed the limits of that technique even for monitoring anesthetic states under certain conditions [START_REF] Takamatsu | Entropy indices vs the bispectral index for estimating nociception during sevoflurane anaesthesia[END_REF]. Then, the fact that raw applications of BIS to recordings performed in epileptic patients failed to show lateralization effects [START_REF] Heller | Bilateral bispectral index monitoring during suppression of unilateral hemispheric function[END_REF][START_REF] Ohshima | Transient decrease in bispectral index without associated changes in the level of consciousness during photic stimulation in an epileptic patient[END_REF] cannot represent an argument against the value of bispectral analysis in its whole. Actually, bispectral analysis was successfully used to detect ischemic cerebral injuries and monitor their course [START_REF] Huang | Discrimination of cerebral ischemic states using bispectrum analysis of eeg and artificial neural network[END_REF].

Our results show that the phase couplings observed in the post-ictal periods tended to occur at frequencies higher than during ictal recordings. Resonances occur as a result of interference between waves traveling in different directions that combine to form standing wave patterns [START_REF] Nunez | Neocortical dynamics and human EEG rhythms[END_REF]. This phenomenon requires that each neural mass has a relatively large number of synapses so that signals are transferred between two locations in a time roughly proportional to the distance between the two locations. In one-dimensional standing waves, a spatial frequency corresponds to each frequency of resonance. In multidimensional waves likely to be generated in a complex structure such as the cerebral cortex, the concept of spatial frequency is not precise but the general idea that high spatial frequencies correspond to high temporal frequencies is preserved [START_REF] Nunez | Neocortical dynamics and human EEG rhythms[END_REF]. Then, a decrease in the index of resonance IR, as usually observed during the ictal periods, indicate a spread of the activity over an extended cortical area. The significant difference between contralateral, with higher frequencies of resonance, and ipsilateral hemispheres clearly indicates that the index IR provides relevant information about the location of the epileptogenic focus. Indeed, the epileptogenic focus appears located in the area with lower resonnant frequencies because this corresponds to the area where the seizure can propagate more easily. This appears as an interesting validation of the interpretation of IR. The observation of specific electrodes showing an opposite course of IR might reveal the transient activation/desactivation of neural circuits induced by seizure dynamics and opens the way of further investigation.

Last but not least, we shall mention the possibility to compare our results with a current source density analysis computing inverse solutions during the intervals of interest. In this case particular attention should be paid to the choice of the reference because it may affect significantly the outcome of the analysis [START_REF] Hagemann | The quest for the eeg reference revisited: A glance from brain asymmetry research[END_REF][START_REF] Tenke | Reference-free quantifiation of eeg spectra: Combining current source density (CSD) and frequency principal components analysis (FPCA)[END_REF]. The current study was primarily aimed at comparing the results between the two hemispheres. The choice of a referential montage to two preauricular electrodes was more dictated by the willingness of computing power maps with larger total power than looking for a precise localization which would have required an ideal infinity reference [START_REF] Dezhong | A comparative study of different references for eeg spectral mapping: the issue of the neutral reference and the use of the infinity reference[END_REF].

In conclusion, the index IR appears as an interesting parameter to evaluate the level of interareal functional connectivity in Fov recordings in epileptic patients, but its usage is likely to be extended in electrophysiological studies.

Figure 1 :

 1 Figure 1: Outline of the unresolving result provided by power spectrum analysis when the recorded signals depend on phase relations more than in frequency relations. (a) Assume that two signals, y(t) and z(t), were recorded simultaneously from separate channels. Each signal was recorded for N epochs of equal time. (b) Calculation of the Fourier transform of each signal. (c) Calculation of the power spectrum for each signal. See text for more details.

Figure 2 :

 2 Figure 2: Foramen ovale electrodes. Relative distribution of the frequencies of resonnance before (a,b), during (c,d) and after seizures (e,f) in the ipsilateral (a,c,e) and contralateral (b,d,f) hemispheres to the epileptic focus. Bin size corresponds to 10 Hz intervals. All values refer to results obtained from Fov electrodes. Frequencies in range 15-30 Hz were classified in the beta band (dark grey) and frequencies in range 40-55 Hz were clasified in the gamma band (light grey).

Table 1 :

 1 Index of resonance (average ± SEM) calculated before, during and after seizure in the ipsilateral and contralateral hemisphere to the epileptogenic focus. The underlined values indicate the only cases characterized by an increase of IR in the ictal periods.

	Lead		Ipsilateral			Contralateral
		pre-ictal	ictal	post-ictal	pre-ictal	ictal	post-ictal
	Fov	0.97 (0.11)	0.62 (0.08)	1.43 (0.15)	0.77 (0.10)	0.55 (0.07)	1.95 (0.21)
	Fp1/Fp2	2.86 (0.22)	1.58 (0.15)	1.86 (0.19)	2.17 (0.21)	0.32 (0.07)	1.98 (0.17)
	F3/F4	1.84 (0.20)	1.57 (0.18)	1.57 (0.19)	0.92 (0.12)	1.87 (0.17)	1.52 (0.10)
	F7/F8	2.13 (0.18)	1.42 (0.14)	2.07 (0.23)	1.66 (0.09)	1.59 (0.08)	2.16 (0.15)
	F9/F10	1.71 (0.15)	0.72 (0.08)	1.76 (0.17)	2.10 (0.20)	0.97 (0.08)	1.17 (0.12)
	T3/T4	2.24 (0.23)	1.00 (0.09)	1.31 (0.15)	1.40 (0.12)	0.63 (0.10)	1.64 (0.17)
	T5/T6	1.29 (0.15)	0.72 (0.09)	1.13 (0.14)	1.64 (0.14)	0.43 (0.07)	1.81 (0.14)
	C3/C4	0.81 (0.09)	1.21 (0.15)	0.95 (0.14)	0.95 (0.12)	0.44 (0.08)	1.31 (0.11)
	P3/P4	1.33 (0.15)	0.78 (0.12)	1.34 (0.16)	0.88 (0.10)	0.55 (0.08)	1.03 (0.12)
	O1/O2	1.00 (0.07)	0.61 (0.08)	1.06 (0.08)	0.69 (0.06)	0.47 (0.07)	1.18 (0.08)
	Index of Resonnance		contra ipsi contra ipsi TUMOR MT SCLEROSIS
	PRE	During	POST
		seizures
	Figure

Acknowledgements

The authors wish to thank the Dept. of Neurology of the Inselspital Bern, Switzerland, for providing the EEG data used for this study and in particular Dr. F. Donati and Dr. Schindler for their help in data management, and M. Kollar for assistance in EEG recording. The project was partially supported by Swiss National Science Foundation grant no. 7-IP-062620.


C Roquelet

D Garrot

J S Lauret
email: lauret@lpqm.ens-cachan.fr

C Voisin

V Alain-Rizzo

Ph Roussignol

J A Delaire

E Deleporte

Quantum efficiency of energy transfer in non-covalent carbon nanotube/porphyrin compounds

We report on the quantum yield of excitation energy transfer in non-covalently bound nanotube/porphyrin compounds. Evidence for energy transfer is gained from photoluminescence excitation experiments. We perform a quantitative evaluation of the transfer quantum yield in the case of (6,5) nanotubes through three independent methods : quantitative PLE measurements, evalu-

ation of the luminescence quenching of the donor (porphyrin) and ultrafast transient absorption measurements. The latter shows a tremendous increase of the porphyrin recovery rate upon incorporation in the compound. All these measurements consistently lead to an exceptional quantum yield efficiency: 1-10 -3 ≤ η ≤ 1-10 -5 .

Functionalization of single-wall carbon nanotubes (SWNTs) is a rapidly developing field in view of applications such as biology imaging [1] or optoelectronics [2][3][4]. In particular, the coupling of dye molecules with nanotubes is of great interest regarding possible photovoltaïc and other optoelectronic applications [2,3,5]. The general motivation is to combine the exceptional transport properties of carbon nanotubes with the versatility of the optical properties of the chromophores. In this context, it is of particular importance to preserve the intrinsic properties of carbon nanotubes such as their high mobility. Therefore usual covalent chemistry, which leads to deep defects formation due to local destruction of the π-electronic system, should be avoided. In contrast, the use of non-covalent chemistry (such as π-stacking interaction) has proven to be compatible with high quality transport and optical properties of the nanotubes [6][7][8]. On the other hand it usually leads to poorly stable compounds [6][7][8]. Recently, an original method based on micelle encapsulation of the nanotube/molecule compound has been demonstrated that allows both stability and minimal perturbation to the nanotube properties [8]. Depending on the band alignment, this coupling can lead to either charge transfer (CT) or excitation energy transfer (EET).

In view of applications, it is important to show that although the compound stability relies on weak interactions, it is possible to have an efficient coupling between the nanotube and the organic molecule.

In this Letter, we study SWNT/porphyrin compounds which are known for showing EET [6][7][8] and we perform a quantitative investigation of the strength of this coupling in the case of (6,5) nanotubes by measuring the quantum yield and the dynamics of the energy transfer. Photoluminescence (PL) experiments conducted on carbon nanotube/porphyrin compounds show unambiguous evidence for EET : the emission of light on the near infra-red (NIR) transitions of the nanotube is strongly enhanced when the excitation is in resonance with absorption lines of the porphyrin molecule. Concomitantly, the fluorescence of the porphyrin is strongly suppressed. In the time domain, the complex shows a reduction by several orders of magnitude of the porphyrin ground state recovery time. Those three independent measurements consistently lead to an exceptional EET quantum yield comprised between 1-10 -3 and 1-10 -5 .

Purified CoMoCAT nanotubes (SouthWest Nanotechnologies, SG65) containing mainly the (6,5) chirality were functionalized with base-free tetraphenyl porphyrin (TPP) by means of the micelle swelling method (see [8] for details). The output of a monochromator illumi-2 nated by a UV-VIS Xenon lamp served as a tunable light source for the photoluminescence excitation experiments (PLE). A step of 10 nm is used for the excitation in the PLE map.

The ultrafast pump/probe experiments were conducted in a degenerate configuration at 2.952 eV and 2.831 eV with a frequency doubled mode-locked Ti:Saphire laser which delivers ∼80 fs pulses at a 86 MHz repetition rate.

FIG. 1: Optical absorption spectra of a water suspension of nanotube in micelles (blue) and of a water suspension of nanotube/porphyrin compounds (grey). Optical absorption spectrum of a micellar suspension of porphyrins rescaled for clarity (black).

Carbon nanotubes display NIR absorption from S 11 excitons (around 1.2 eV) and visible absorption from S 22 excitons near 2 eV (Figure 1, blue line). For the SWNT/TPP compounds (Figure 1, grey line), these lines are red-shifted of about 20 meV as discussed in [6][7][8]. The main absorption line of the compound (the so-called Soret absorption band of the porphyrin) is observed at 2.831 eV. It corresponds to ground state absorption to the second electronic excited state of the porphyrin in the compound. The shoulder at 2.952 eV is a signature of residual free porphyrins embedded in micelles (to be compared to free porphyrin absorption spectrum, black line in Fig. 1) [8]. The transitions to the first electronic excited states (Q bands, around 2 eV) are barely visible in the compound since they are much weaker and further overlap with the S 22 excitonic absorption of the nanotubes. Figure 2a) displays the PLE map of the nanotube suspension. One spot predominates in this map. The semi-empirical formula of Bachilo et al. allows to assign this spot to the (6,5) family [9]. Additional faint spots are present that correspond to weakly abundant chiral families. The PLE map of the nanotube/porphyrin compound suspension is shown in Figure 2b). The spot corresponding to (6,5) nanotubes is red-shifted both in excitation and emission energies. This shift results from a dielectric screening of the excitonic transition by the porphyrin molecules [10]. Compared to the PLE map of nanotubes, additional spots are visible along the vertical dashed line for excitation energies of 2.805 and 2.357 eV. The spot at (x=1.240 eV, y=2.805 eV) corresponds to absorption on the Soret-band and emission by nanotubes. This brings evidence for excitation energy transfer from the porphyrin to the nanotube: when photons are absorbed by the porphyrin molecules, the luminescence of the nanotube is enhanced [6][7][8]. We assign the PLE feature at an excitation energy of Importantly, the intensity of the intrinsic PLE peak on the S 22 transition of (6,5) nanotubes is on the same order than the PLE peak through EET from the Soret band (upper and lower peaks along the PLE line-cut in Fig. 2b). This allows quantitative investigation of the transfer yield. The PLE peak amplitude of nanotubes is related to their absorption cross-section σ S 22 (1.1 ± 0.1×10 -12 cm 2 .µm -1 ) for (6,5) nanotubes [11], since it is well established that the internal conversion from S 22 to S 11 is ultrafast and efficient [12,13]. On the other hand, the PLE peak at 2.805 eV (EET) is related to the absorption cross-section of the porphyrin (σ T P P = 7 × 10 -16 cm 2 ) [14], the surface coverage of the nanotube by TPP molecules (α) and the transfer yield (η). The equal amplitude of the two PLE peaks leads to the following relationship:

σ T P P × N × η = σ S 22 with N = α S N T

S T P P

where S T P P 1.22 nm 2 is the surface of one TPP molecule and S N T is the wall surface per micron length of a (6,5) nanotube. We find that ηα = 0.95 ± 0.10. The synthesis process ensuring that the coverage is close to one [8], we deduce that the transfer yield must also be on the order of one.

Another independent manner for evaluating this quantum efficiency is given by the quenching of the luminescence of the donor. Figure 3a) shows the visible luminescence of free porphyrins (black curve) and of the complex (grey curve) with the same porphyrin concentration and incident power. Both spectra display identical bands at 1.719 eV and 1.900 eV but the photoluminescence of the complex is reduced by a factor 750 for the complex. However, the position of the lines in the compound shows that the residual luminescence actually arises from left after porphyrin rather than from the compound itself since the bands of the latter should be red shifted by ∼ 50 meV. This assignment is further confirmed by PLE measurements: again the excitation spectrum of this residual PL (Figure 3b)) is identical to the one of free porphyrin whereas the redshift of the Soret band is of 120 meV for the compounds (See Figure 1). When looking specifically for PL of the compound by tuning the excitation at 2,818 eV, we cannot detect any signal within our detectivity which is limited by the tail emission of free porphyrin. Assuming that any signal from the compound would be detected if of intensity comparable to this tail emission, we deduce I d-a I d ≤ 9.10 -4 where I d-a (resp. I d ) is the integrated PL intensity of the donor in presence (resp. absence) of the acceptor. Since the quantum efficiency of the EET process can be written:

η = 1 -I d-a I d we can give a lower bound of η : η ≥ 1 -10 -3 .
Finally, ultrafast pump/probe experiments allowed us to gain further insight into the dynamics and therefore into the transfer yield of this EET. In these experiments, both pump and probe were tuned in resonance with the Soret band of the porphyrin (at 2.952 eV for the free porphyrin or at 2.831 eV for the compound). Free porphyrin shows a bi-exponential recovery dynamics (Figure 3c) with a main very slow component (unresolved here) that was reported to be on the order of 12 ns in previous studies [15]. This component corresponds to the ground state recovery. In nanotube/porphyrin compounds, this recovery time is dramatically reduced down to ∼120 fs. This decrease of the donor life-time is typical of an efficient donor-acceptor coupling. The ratio τ d-a τ d , where τ d (resp. τ d-a ) is the recovery time of the free (resp. in compound) porphyrin is on the order of 10 -5 and is related to the efficiency η by:

η = 1 -τ d-a τ d = 1 -10 -5
In summary, we have reported on efficient and ultrafast excitation energy transfer in nanotube/porphyrin assemblies. The quenching of the porphyrin luminescence and the tremendous increase of its relaxation rate show that the efficiency of the EET process is very high. Cross-estimates of this quantum yield lead to 1 -10 -3 ≤ η ≤ 1 -10 -5 . This result is especially strong for non-covalently bound compounds. This opens avenues for creating molecular assemblies based on nanotubes that preserve the nanotube intrinsic properties and nevertheless show efficient coupling to the chromophore for light-harvesting or photovoltaïc applications.

  2.357 eV to EET upon absorption on the porphyrin higher Q band, red shifted of about 50 meV in comparison with free porphyrins. The other Q bands could not be evidenced in PLE measurements, most probably because of spectral overlap with the nanotubes S 22 transitions. Nevertheless, the observation of the 2.357 eV PLE feature means that the EET occurs at least partially through the Q bands of the porphyrin molecules.

FIG. 2 :

 2 FIG. 2: PLE maps of a) the nanotube suspension; b) the nanotube/porphyrin compound suspension. The yellow dashed line corresponds to a PLE line-cut.

FIG. 3 :

 3 FIG. 3: a) Photoluminescence spectra of free porphyrins (black curve) and of the nanotube/porphyrin compounds (grey curve) excited on their respective Soret band. b) NormalizedPLE detected 1.722 eV in free porphyrins (black curve) and in the nanotube/porphyrin compound (grey curve). c) Relative change of transmission as a function of the time delay for pump and probein resonance with the Soret band of the free porphyrins (black curve) or in resonance with the Soret band of the compounds (grey curve). Green and blue dashed lines are bi-and mono-exponential fits respectively.

This work was supported by the GDR-E "nanotube" (GDRE2756), grant "C'Nano IdF EPONAD" from "Région Ile de France" and ANR grant "CEDONA".


Wendell O Rodrigues
email: wendell.rodrigues@inria.fr

Frédéric Guyomarc'
email: frederic.guyomarch@inria.fr

Yvonnick Le Menach
email: yvonnick.le-menach@univ-lille1.fr

Jean-Luc Dekeyser
email: jean-luc.dekeyser@lifl.fr

Parallel Sparse Matrix Solver on the GPU Applied to Simulation of Electrical Machines

Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which need speed-up on their solution. This paper examines the parallelism of sparse matrix solver on the graphics processors. More specifically, we implement the conjugate gradient technique with input matrix stored in CSR, and Symmetric CSR and CSC formats. This method is one of the most efficient iterative methods available for solving the finite-element basis functions of Maxwell's equations. The GPU (Graphics Processing Unit), which is used for its implementation, provides mechanisms to parallel the algorithm. Thus, it increases significantly the computation speed in relation to serial code on CPU based systems.

I. INTRODUCTION

An electromagnetic field analysis is one of the most complex problems of physics. And, the modeling and simulation of electrical systems use a very large computational algorithms to solve their problems. One of this algorithms is based on the conjugate gradient (CG) method [START_REF] Saad | Iterative methods for sparse linear systems[END_REF]. The CG method is an effective technique for symmetric positive definite systems. It is suitable for systems of the form Ax=b, where A is a known, square, symmetric, positive-definite matrix, x is a unknown solution vector and b is a known vector. Iterative methods like CG are suited for use with sparse matrices.

The solution of large, sparse linear systems of equations is the single most computationally expensive step. Thus, any reduction in the linear system solution time will result in a significant saving in the total process time. This need demands for algorithms and software that can be used on parallel processors.

This paper describes the use of the GPU as platform to implement a CG method to solve a linear system. The sample inputs are matrix stored in Symmetric CSR (compressed sparse row) [START_REF] Saad | Iterative methods for sparse linear systems[END_REF] format obtained from a simulation of electric machines. The algorithms use standard BLAS library and two implemented kernels for matrix-vector product (SpMV). The next section describes the GPU which is the platform used and how to program it with CUDA. Section 3 depicts the matrix used and how to implement the solver. A execution performance is discussed in following section. Finally, some concluding remarks are made about obtained results.

II. GPU

GPU is a manycore processor attached to a graphics card dedicated to calculating floating point operations. Even if GPUs are a manycore processors, their parallelism continues to scale with Moore's law. It is necessary to develop application software that transparently scales its parallelism. CUDA (Compute Unified Device Architecture) [START_REF]NVIDIA CUDA Compute Unified Device Architecture Version 2[END_REF] is a parallel programming model and software environment designed to overcome this challenge while maintaining a low learning curve for programmers familiar with standard programming languages such as C.

A. Processor Architecture

The GPU devotes more transistors to data processing rather data caching and flow control. This is the reason why the GPU is specialized for compute intensive. NVIDIA GPU, more precisely, is composed of array of SM(Streaming Multiprocessors), each one is equipped with 8 scalar cores (the SP or Streaming Processors), 16834 32-bit registers, and 16KB of high-bandwidth low-latency memory shared for up to 1024 coresident threads. GPUs such as the NVIDIA GeForce GTX 280 contain 30 multiprocessors, so 30K threads can be created for a certain task. Further, each multiprocessor executes groups, called warps, of 32 threads simultaneously.

B. Memory Architecture

In the NVIDIA GPU memory model, there are per-thread local, per-block shared, and device memory which comprehends global, constant, and texture memories. Shared Memory can be only accessed by threads in the same block. Because it is on chip, the Shared Memory space is much faster than the local and Global Memory spaces. But only 16KB of shared memory are available on each SM.

C. CUDA Programming Model

CUDA is a C language extension developed by NVIDIA to facilitate writing programs on GPUs. It allows the programmer to define C functions, called kernels, that, when called, are executed N times in parallel by N different CUDA threads, as opposed to only once like regular C functions. One of the main features of CUDA is the provision of a Linear Algebra library(CuBLAS) and an Fast Fourier Transform library (CuFFT) [START_REF]NVIDIA CUDA Compute Unified Device Architecture Version 2[END_REF]. The next section describes the implementation of CG on the GPU and the use of CuBLAS library.

III. IMPLEMENTATION

The Conjugate Gradient was applied to 30880x30880 symmetric sparse matrix A with 449798 nonzero double precision elements. It is stored in full or symmetric CSR format files which include the unknown elements vector x and the result vector b. The CG algorithm used to implement the program is below. Require: init variables 1: for all k such that 1 ≤ k ≤ N do 2:

α ⇐ (r T r)

(p T Ap) 3: x ⇐ x + αp 4: break if convergence 5: r ⇐ r -αAp 6: β ⇐ (r T k r k ) (r T k-1 r k-1 )
7:

p ⇐ r + βp 8: end for All the internal loop operations are executed on GPU. The scalar product and axpy functions on lines 3,5,7 use CuBLAS functions. Since BLAS is only for dense matrix, naturally it is necessary to create a CUDA kernel for sparse matrix. For that reason, a SpMV algorithm for matrix-vector multiplication should be implemented to execute the Ap product on line 2. Let A = (L + D + U ), where D is the main diagonal part of A, L is its strictly lower triangular part and U is its strictly upper triangular part. Since A is symmetric, U T = L. Thus, A can be stored in CSR format of (L + D).

Three algorithms were implemented in this work. The first one is a trivial solution of y = Ax in which each thread executes y

[tid]+ = A[i -1] * x[jA[i -1] -1],
where tid is the thread identify, and [i,jA] are obtained from vectors of the stored matrix in compressed form. The two other solutions explore the symmetry characteristic. The aim is to cut down the time and memory allocation cost. The figure 1 shows the procedure of algorithm conception. The kernels are composed of blocks and each block has certain threads. Only one kernel can execute in same time on same device and there are a few blocks in execution simultaneously in each SM. Sequentially the kernel 1(SCSR) and kernel 2(SCSC) are executed and they take care of L + D and U respectively. To avoid writing conflicts on y vector in global memory, the kernel 2 calls atomic functions and that allows just one thread write in a memory address at given moment. As the number of elements of a column or a row can be greater than the number of threads in a block, it is necessary that the algorithm calculates the quantity of elements for each thread.

IV. RESULTS

A double precision version of CG was created on a contemporary conventional CPU and this one was used as a reference to calculate the speed-up. Two other versions were developed on the GPU. The first one is a single precision version which was tested on a NVIDIA Tesla C870 card. The second one is The matrix reading from files takes time to be done properly. Approximately 6ms in our tests. Because this operation is basic for all experiments, it is not necessary to evaluate it. It is important to examine the Scalar Product, AXPY, and SpMV execution time because these functions are called repetitively in each loop interaction. Yet, all the time that the interactive CG loop takes. The table I shows the operations and their respective spent time values. The application not use the sym SpMV, its times are there just for benchmarking. V. CONCLUSION This approach issues the viability of using GPU on sparse matrix solvers. The obtained results allow us to evaluate two important impacts in finite-element method of Maxwell's equations using Conjugate Gradient algorithm. The first one is concerned to speed gain. On the GPU, the CG arrives faster than on the CPU due its parallel architecture. The second one is the impact of storing symmetric matrix in memory. Although it can store in memory almost half of the matrix, the performance of algorithm decreases as shown in table of speed-up results. This is due the repetitive way that the kernel computes and accumulates the y = Ax result. However, both cases contribute significantly to accelerate the computation of basis functions.

Fig. 1 .

 1 Fig. 1. SpMV on Symmetric CSR and CSC storage format


V Péron

G Caloz

M Dauge

Skin-Effect Description in Electromagnetism with a Scaled Asymptotic Expansion

We study a transmission problem in high contrast media. The 3-D case of the Maxwell equations in harmonic regime is considered. We derive an asymptotic expansion with respect to a small parameter δ > 0 related to high conductivity. This expansion is theoretically justified at any order. Numerical simulations highlight the skin-effect and the expansion accuracy.

Introduction

We consider the diffraction problem of waves by highly conducting materials in electromagnetism. The high conductivity reduces the penetration of the wave to a boundary layer, see [START_REF] Haddar | Construction and analysis of approximate models for electromagnetic scattering from imperfectly conducting scatterers[END_REF]. The physical model is the following. Ω cd is an open bounded domain in R 3 with connected complement, occupied by a conducting medium. Ω cd is embedded in an insulating medium Ω is . We suppose that their common interface Σ is smooth. We define Ω = Ω cd ∪ Σ ∪ Ω is . We denote by δ a small parameter which is inversely proportional to the square root of the conductivity σ. The depth of the boundary layer is proportional to δ. We first give the formal construction of the asymptotic expansion. Then, we prove optimal error estimates. Finally, we present numerical simulations in axisymmetric geometry.

Scaled asymptotic expansion

Eliminating the magnetic field H δ from Maxwell equations, we perform a study in electric field E δ .

Normal coordinates

To describe the boundary layer in Ω cd , we define a local normal coordinate system (y α , y 3 ), α ∈ {1, 2}, in a tubular neighborhood O of Σ, y 3 ∈ (0, h 0 ). The euclidian metric in O is denoted by (g ij ) i,j∈{1,2,3} . We adopt the tensorial calculus, see [START_REF] Faou | Elasticity on a thin shell: Formal series solution[END_REF], to write Maxwell equations in these coordinates. The curl operator writes

(curl E) α = 1 √ g 3βα (∂ 3 E β -∂ β E 3 ) (curl E) 3 = 1 √ g 3αβ D h α E β with g = det(g ij ),
ijk the Levi-Civita symbol, and D h a covariant derivative defined for h = y 3 , see [START_REF] Faou | Elasticity on a thin shell: Formal series solution[END_REF].

Scaling and ansatz

We perform the scaling Y 3 = y 3 δ in O, and expand the 3D Maxwell operator in power of series of δ. This leads to postulate the following expansions

E is δ (x) ∼ j≥0 E is j (x)δ j , E cd δ (x) ∼ j≥0 E cd j (x; δ)δ j (1)
respectively in Ω is , and Ω cd , with E cd j (x; δ) = W cd j (y α , y 3 δ ) when (y α , y 3 ) ∈ O. We prove that W cd 0 = 0, and

W cd j (., Y 3 ) = exp(-λY 3 )[a 0 + .. + a j-1 Y j-1 3
], with (λ) > 0. According to Faraday's law H δ = 1/(iκµ 0 ) curl E δ , κ > 0 (a wave number), we derive the expansion of the magnetic field.

Uniform a priori estimate

A regularized variational formulation of our problem in the domain Ω using the space

X N (δ) = {E ∈ H(curl, Ω)| ε(δ)E ∈ H(div, Ω), E × n = 0 on ∂Ω} is: Find E δ ∈ X N (δ) such that for all u ∈ X N (δ) Ω curl E•curl u+div ε(δ)E div ε(δ)u-κ 2 ε(δ)E•udx = Ω (F δ • u - 1 κ 2 div F δ div ε(δ)u)dx, (2)
with

ε(δ) = 1 µ 0 (1 Ω is + (1 + i δ 2 )1 Ω cd )
, µ 0 > 0, and F δ ∈ H(div, Ω). Under a spectral hypothesis on κ, we prove that ∃ δ 0 > 0 small enough such that ∀δ ∈ (0, δ 0 ), ( 2) has a unique solution E δ ∈ X N (δ), and there is a constant C > 0 independent of δ such that

curl E δ 0,Ω + div ε(δ)E δ 0,Ω + E δ 0,Ω + 1 δ E δ 0,Ω cd ≤ C F δ H(div,Ω) .
We prove this estimate using a technique of vector potential, see [START_REF] Amrouche | Vector Potentials in Threedimensional Non-smooth Domains[END_REF]. Defining R δ m from (1) by removing to E δ the m + 1 first-terms of the expansion, we deduce optimal error estimates for the truncated expansions

R δ m H(curl,Ω) + div ε(δ)R δ m 0,Ω + 1 δ R δ m 0,Ω cd ≤ Cδ m-1 .
3 Numerical simulations Here we present numerical experiments to illustrate the accuracy of the asymptotic expansion. We perform our analysis to the magnetic field and restrict ourselves to axisymmetric domains with an orthoradial data. After having meshed the domain, we compute the orthoradial component of the magnetic field H θ with the finite element library Melina, see [4]. The numerical method uses a variational form with unknown H θ (r, z) in a meridian domain, which is meshed in such a way the boundary layer is correctly taken into account, see Figure 1 for spheroidal domains. We extract values of |H θ (y 3 )|

Figure 1 :

 1 Figure 1: | H θ | for σ = 5 S.m -1 and 80 S.m -1

Figure 2 :- 3 ,Figure 3 :

 233 Figure 2: log 10 |H θ (2 -r)| for σ = 5 S.m -1


Gabriel Caloz
email: gabriel.caloz@univ-rennes1.fr

Monique Dauge
email: monique.dauge@univ-rennes1.fr

Erwan Faou
email: erwan.faou@inria.fr

Victor Péron
email: victor.peron@inria.fr

Victor Péron Skin

Chile Concepcion

Inria-

Skin Effect in Electromagnetism and Asymptotic Behaviour of Skin Depth for High Conductivity

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

SKIN EFFECT IN ELECTROMAGNETISM AND ASYMPTOTIC BEHAVIOR OF SKIN DEPTH FOR HIGH CONDUCTIVITY

G. CALOZ, M. DAUGE, E. FAOU, AND V. P ÉRON Abstract. We study a three-dimensional model for the skin effect in electromagnetism, [START_REF] Caloz | Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism[END_REF][START_REF] Haddar | Generalized impedance boundary conditions for scattering problems from strongly absorbing obstacles: the case of Maxwell's equations[END_REF][START_REF] Péron | Modélisation mathématique de phénomènes électromagnétiques dans des matériaux à fort contraste[END_REF]. The 3-D case of the Maxwell equations in harmonic regime on a domain composed of a dielectric and of a highly conducting material is considered. We derive an asymptotic expansion with respect to a small parameter related to high conductivity. This expansion is theoretically justified at any order. The asymptotic expansion and numerical simulations in axisymmetric geometry exhibit the influence of the geometry of the interface on the skin effect. We first prove uniform a priori estimates for a scalar transmission problem with constant coefficients on two subdomains, when the ratio between these coefficients is large. Then, we prove uniform a priori estimates for Maxwell transmission problem, [START_REF] Caloz | Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism[END_REF][START_REF] Péron | Modélisation mathématique de phénomènes électromagnétiques dans des matériaux à fort contraste[END_REF]. The technique is based on an appropriate decomposition of the electric field, which gradient part is estimated thanks to the first part. Next, we derive a multiscale asymptotic expansion for the solution of the harmonic Maxwell equations, with a regular interface between them. With the help of the uniform estimates, we prove the convergence of the asymptotic expansion as the conductivity tends to infinity. To measure the skin effect, we introduce a suitable function defined on the interface and generalizing the classical skin depth. We prove an asymptotic expansion at high conductivity for this function, which demonstrates the influence of the geometry of the interface on the skin depth, see [START_REF] Dauge | Comportement asymptotique à haute conductivité de l'épaisseur de peau en électromagnétisme[END_REF].

Keywords: asymptotic analysis, electromagnetic waves, boundary layer, skin effect Mathematics Subject Classifications (2000): 35J05, 78A45, 78M10, 78M35