Julie Quenouille

Ludovic Saint-Felix

Benoit Moury

Alain Palloix
email: alain.palloix@avignon.inra.fr

Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus

Keywords: Durability of resistance, genetic background, core-collection, Capsicum annuum, genetic background

The evolution of resistance-breaking capacity in pathogen populations was shown to depend on the plant genetic background surrounding the resistance genes. We evaluated a core-collection of pepper (Capsicum annuum) landraces, representing the worldwide genetic diversity, for its ability to modulate the breakdown frequency by Potato virus Y, of major resistance alleles at the pvr2 locus encoding the eukaryotic initiation factor 4E (eIF4E).

Depending on pepper landrace, the breakdown frequency of a given resistance allele varied from 0% to 52.5%, attesting their diversity and the availability of genetic backgrounds favorable to resistance durability in the plant germplasm . The mutations in the virus genome involved in resistance breakdown also differed between plant genotypes, indicating differential selection effects exerted on the virus population by the different genetic backgrounds. The breakdown frequency was positively correlated to the level of virus accumulation, confirming the impact of quantitative resistance loci on resistance durability. Among these loci, pvr6, encoding an isoform of eIF4E, was associated with a major effect on virus accumulation and on the breakdown frequency of the pvr2 mediated resistance. This exploration of plant genetic diversity delivered new resources for the control of pathogen evolution and the increase of resistance durability.

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The main limit to the use of resistant cultivars is the capacity of pathogens to counteradapt and overcome plant resistances. In this context, many research efforts were devoted to handle adaptation of plant pathogen populations and maintain the durability of resistant cultivars [START_REF] Kiyosawa | Genetics and epidemiological modeling of breakdown of plant disease resistance[END_REF]Wolfe, 1985;Mundt et al., 2002;Pink, 2002;[START_REF] Mcdonald | Pathogen population genetics, evolutionary potential, and durable resistance[END_REF].

In several pathosystems involving virus, oomycete or nematode plant parasites, the durability of major resistance genes was experimentally shown to be dependent on the genetic background in which it was introgressed (Acosta-Leal andXiong 2008, 2013;Palloix et al., 2009;[START_REF] Brun | Quantitative resistance increases the durability of qualitative resistance to Leptosphaeria maculans in Brassica napus[END_REF][START_REF] Fournet | Selection of nematodes by resistant plants has implications for local adaptation and crossvirulence[END_REF]. In these studies, the breakdown frequency of the major resistance gene decreased when introgressed into a partially resistant cultivar, suggesting that the partially resistant genetic background was favourable to control pathogen evolution and enhance the durability of major resistance genes.

In the plant-virus system Potato virus Y (PVY)/pepper(Capsicum annuum), the protective effect of the genetic background on the breakdown frequency of the pvr2 3 gene, causing resistance to this virus, was mostly due to the additional level of quantitative resistance reducing the viral accumulation (Quenouille et al., 2012). The breakdown frequency of the major gene was shown to be highly heritable (i.e. it was mainly under genetic control) and affected by four QTLs (Quenouille et al., 2014). These results, obtained on a narrow plant genetic basis, i.e. in a progeny between two Capsicum annuum lines, opened new ways for sustainable resistance breeding, but little is known on the availability of such QTLs and the frequency of favorable backgrounds in the plant genetic resources.

In this context, the aim of our study was to estimate the availability and diversity of genetic backgrounds increasing the durability of the pvr2-mediated resistance on a broader genetic scale in pepper resources and to confirm (or not) the relationship with factors affecting quantitative resistance. Our strategy was to select a core-collection of pepper landraces from

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different origins but carrying two closely related pvr2 alleles and to measure the resistance breakdown frequencies in these pepper accessions on the one hand, and the level of quantitative resistance controlled by their genetics backgrounds on the other hand.

Selection of the core-collection.

The pepper (Capsicum spp.) germplasm collection maintained at INRA Unité de Génétique et Amélioration des Fruits et Légumes was screened for resistance to PVY and 35.7% of the 862 tested accessions were found to be resistant (Sage-Palloix et al., 2007). A subset of 107 resistant accessions was chosen while maximizing the diversity of their geographic origins, and were sequenced for the pvr2 resistance allele. Twenty-one accessions carried the pvr2 3 allele, which was the most frequent allele, and five carried the pvr2 4 allele (Charron et al., 2008 and personal communication). The sequence of the eIF4E protein (eukaryotic initiation factor 4E) encoded by these two pvr2 alleles differs only by one aminoacid substitution at position 205 (a glycine for pvr2 3 and an aspartic acid for pvr2 4 ). They displayed the same resistance specificity towards seven different PVY variants and were easily broken down compared to other pvr2 alleles (Ayme et al., 2007;[START_REF] Charron | Natural variation and functional analyses provide evidence for co-evolution between plant eIF4E and potyviral VPg[END_REF][START_REF] Moury | Interaction patterns between Potato virus Y and eIF4E-mediated recessive resistance in the Solanaceae[END_REF]. To further test the durability of the pvr2 alleles in these different genetic backgrounds, we selected the accessions which were homozygous for pvr2 3 (16 accessions) or pvr2 4 (4 accessions), while discarding the closely related accessions with identical genotypes at the tested SSR loci (Nicolaï et al., 2013) , resulting in a final set of 20 Capsicum annuum inbred lines issued from American, African and Asian pepper landraces (table 1). The genetic diversity of this set of 20 C. annuum lines was compared to the genetic diversity of the entire C. annuum germplasm collection which includes 1063 accessions from 89 different countries, using 28 simple sequence repeat (SSR) loci (Nicolaï et al., 2013). The wide distribution of the 20 inbred lines retained for resistance analysis across the phylogenetic tree representing the

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whole collection attested for their high diversity and poor genetic structuration (Fig. 1). No shared origin was evidenced for the accessions carrying pvr2 3 , which were widespread in the different parts of the tree, corresponding to large sweet or small and pungent fruited pepper landraces from diverse geographic origins. The four accessions carrying pvr2 4 were loosely grouped in the distal part of the tree, corresponding to small fruited pepper landraces. Breakdown frequency of the resistance controlled by pvr2 3 or pvr2 4 in the core collection.

To measure the resistance breakdown frequency (RB frequency) of pvr2 3 or pvr2 4 (pvr2 3/4 ), a recombinant PVY, the "CI chimera" was mechanically inoculated to sixty seedlings per accession at the two expanded cotyledon stage in a climate-controlled room at 20-22°C and 12h light/day. The CI chimera is a derivative of the SON41p infectious cDNA clone where the CI-coding region was substituted with that of the LYE84.2 infectious cDNA clone, both clones corresponding to isolates of the C1 clade of PVY [START_REF] Montarry | Genetic background matters: a plant-virus gene for gene interaction is strongly influenced by genetic contexts[END_REF].

This "CI chimera" was chosen because of its higher ability to break the pvr2 3 resistance down compared with the parental clones, allowing more precise estimations and comparisons of the resistance durability of different plant genotypes [START_REF] Montarry | Genetic background matters: a plant-virus gene for gene interaction is strongly influenced by genetic contexts[END_REF]. The CI chimera is not infectious per se toward plants carrying pvr2 Wonder (carrying the pvr2 + susceptibility allele) was used as virus infectivity control and the DH285 inbred line, carrying the pvr2 3 resistance allele and previously known for its high pvr2 3 RB frequency (Palloix et al. 2009) was used as a control for pvr2 3 RB capacity by the CI chimera. Fourteen days post inoculation (dpi), all Yolo Wonder plants showed mosaic symptoms in apical leaves and all plants carrying pvr2 3/4 were symptom free. Mosaic or necrotic symptoms further appeared along the testing period in apical leaves of part of the plants of some pvr2 3/4 accessions. At 35 dpi, three uninoculated leaves were sampled from each plant and pooled to test the presence of PVY by double antibody sandwich-enzymelinked immunosorbent assay (DAS-ELISA). In these conditions, each case of systemic infection in plants carrying the pvr2 3 resistance allele was shown to result from the selection of at least one PVY variant carrying a RB mutation(s) in the VPg cistron [START_REF] Montarry | Genetic background matters: a plant-virus gene for gene interaction is strongly influenced by genetic contexts[END_REF]. For each accession, the RB frequency was calculated by the frequency of systemically infected plants amongst inoculated plants. In this test, 80% of the DH285 resistant plants were broken down, attesting the high capacity of the CI chimera to break the pvr2 3 resistance down in the test conditions. Among the 20 accessions, the RB frequency of pvr2 3/4 varied from 0%

to 52.5% (table 1), with highly significant differences between accessions (Pearson Chi² test, P<0.001). The 20 accessions were classified into two groups (pairwise Fisher exact tests at 5% type-I error threshold after Bonferroni correction). For 18 accessions, the pvr2 3/4 resistance was not, or rarely broken down (RB frequency 5%) and for the two accessions PI369940 and G4, the pvr2 3/4 resistance was frequently broken down (40% and 52.5%, respectively). For PI369940 and G4, all infected plants were checked for the presence of RB mutations in the PVY VPg cistron: total RNA was extracted and the PVY VPg cistron was amplified by reverse transcription-polymerase chain reaction (RT-PCR) and sequenced according to [START_REF] Moury | Interaction patterns between Potato virus Y and eIF4E-mediated recessive resistance in the Solanaceae[END_REF]. For one and four infected plants of G4 and PI369940, respectively, we failed to sequence the PVY VPg cistron. For the other 30 G4 and 20

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PI369940 infected plants, all VPg sequences obtained differed from the initial VPg sequence of CI chimera by only one amino acid substitution. Four of the mutations detected were previously known to result in the breakdown of pvr2 3 resistance [START_REF] Ayme | Different Mutations in the Genome-Linked Protein VPg of Potato virus Y Confer Virulence on the pvr23 Resistance in Pepper[END_REF], four were previously observed in pvr2 3 RB PVY populations and are strongly suspected to be responsible for RB [START_REF] Montarry | Genetic background matters: a plant-virus gene for gene interaction is strongly influenced by genetic contexts[END_REF], and one was never observed before but located at the same codon position (119) as three other observed mutations, suggesting also its involvement in RB (supplementary data I). Five G4 plants and one PI369940 plant were infected by a mixture of two single VPg mutants. These results confirmed the correspondence between systemic infection of plants carrying pvr2 3/4 resistance allele after inoculation by CI chimera and occurrence of RB events. The high RB frequency was not associated with a particular allele at the pvr2 locus since PI369940 carries pvr2 3 and G4 carries pvr2 4 , suggesting that the differences observed between accessions more probably result from the effect of the plant genetic background. The low RB frequencies observed in 18 landraces indicated that genetic backgrounds favorable to the durability of pvr2-mediated resistances are frequent among the genetic resources of pepper.

Differential selection pressure exerted by the plant genetic background

In a previous study [START_REF] Montarry | Genetic background matters: a plant-virus gene for gene interaction is strongly influenced by genetic contexts[END_REF], 67% of the pvr2 3 RB events in DH285 were associated to the selection of the aspartic acid to asparagine codon substitution at position 119 of the VPg cistron of PVY (named VPg-N mutation). In our test, we checked the presence of the VPg-N mutation in 25 infected DH285 plants by dCAPS analyses as described in [START_REF] Montarry | Genetic background matters: a plant-virus gene for gene interaction is strongly influenced by genetic contexts[END_REF]. Results showed that 64% of RB events of DH285 plants were associated to the presence of the VPg-N mutation (table 2), which is not significantly different from the previous results (p-value = 0.13, Fisher exact test). In G4 and PI369940 plants, the percentages of RB events associated with the selection of the VPg-N mutation were equal to

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Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury 55% (17/31) and 29% (7/24) respectively (dCAPS analyses showed the absence of the VPg-N mutation in the five PVY populations from G4 or PI369940 plants for which the full sequence of the VPg cistron was not determined, Suppl. data 1). As a whole, this revealed a significant difference between PI369940 and DH285 (p=0.020, Fisher exact test) but not between PI369940 and G4 (p=0.10) or G4 and DH285 (p=0.41) for the proportion of RB events associated with selection of the VPg-N mutation. This variation cannot be associated to the effect of the pvr2 allele, since both PI369940 and DH285 carry pvr2 3 (and differ in the selection of VPg-N mutation), whereas G4 (pvr2 4 ) and DH285 (pvr2 3 ) did not differ in their preferential selection of the VPg-N mutation. The difference observed between PI369940 and DH285 can be associated to the genetic background which selects more or less frequently the VPg-N mutation. This result showed that various plant genetic backgrounds can exert differential selection pressure on RB mutants, leading to differential frequencies of selection of the various virulent mutants toward the same resistance allele.

Quantitative level of resistance controlled by the genetic background of the pepper accessions.

It was previously shown that a large part of the variation of the RB frequency of pvr2 3 observed in a biparental progeny could be attributed to the level of quantitative resistance et al., 2000;[START_REF] Moury | Survey of Prunus necrotic ringspot virus in rose and its variability in rose and Prunus spp[END_REF]Pagán et al., 2007;[START_REF] Araya | Symptom severity and viral protein or RNA accumulation in lettuce affected by big-vein disease[END_REF] and reveals different levels of tolerance between the 20 pepper accessions.

Here, tolerance is defined as the capacity of the host plant to reduce the effect of an increase of virus accumulation on the plant fitness or damages (Råberg et al., 2007). In order to evaluate if the resistance or tolerance level of the 20 accessions could affect the durability of the pvr2-mediated resistance, we looked at the relationship between VA or AUDPC and the frequency of pvr2 3/4 RB. Two cultivars (G4 and PI369940) presented a high relative VA (>2.0) and simultaneously a high RB frequency (40%), whereas all other cultivars had a low

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VA (<1.1) and a low RB frequency (5%) (Table 1). This resulted in a highly significant positive correlation between VA and the frequency of pvr2

Association between a locus in the pepper genome and pvr2 3/4 RB frequency

In the doubled haploid progeny issued from the F 1 hybrid between the two pepper inbred lines Yolo Wonder and Perennial, we showed that the pvr6 gene encoding eIFiso4E, an isoform of the eIF4E encoded by the pvr2 gene, co-located tightly with a major QTL (R²=0.40) affecting the pvr2 3 RB frequency and a major QTL (R²=0.35) affecting viral accumulation (Quenouille et al., 2014). For these two QTLs located at the pvr6 locus, the Perennial alleles strongly increased the frequency of the pvr2 3 RB and VA. However, this effect was shown to be compensated by additional QTL-alleles from the Perennial genetic

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Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury expression of the eIF4E encoded by pvr2 3/4 due to the absence of the eIFiso4E isoform encoded by pvr6, as shown in Arabidopsis thaliana [START_REF] Duprat | The Arabidopsis eukaryotic initiation factor (iso)4E is dispensable for plant growth but required for susceptibility to potyviruses[END_REF]. Indeed, this higher eIF4E expression could increase its availability for PVY replication and/or translation, maybe by reducing competition effects between PVY VPg and the cap of plant mRNAs [START_REF] Michon | The potyviral virus genome-linked protein VPg forms a ternary complex with the eukaryotic initiation factors eIF4E and eIF4G and reduces eIF4E affinity for a mRNA cap analogue[END_REF]. In turn, higher virus multiplication would lead to higher VA in case of a RB PVY mutant, and higher probability to generate RB mutants in case of a wild-type PVY. However, such hypothetical mechanism still has to be demonstrated and functional validation of the involvement of pvr6 in RB and VA will help in this exploration. The compensatory effect by additional resistance QTLs from Perennial were shown to act at several levels (Quenouille et al. 2012): they were shown to directly reduce virus accumulation, but also to increase the number of viral mutations required for RB. Endly, they slowed down the selection and fixation of RB-mutations in the PVY population.

Conclusion

This study provides the first evaluation of the availability, in plant genetic resources, of genetic backgrounds affecting the durability of major resistance genes. Among a corecollection of 20 pepper accessions, we observed a high diversity of quantitative resistance and of tolerance levels conferred by the genetic background. In term of durability of the pvr2 3 and pvr2 4 major resistance alleles, the pepper accessions were divided into two groups, either with no or rare breakdown or with frequent breakdown, the latter group including only two pepper accessions. The genetic backgrounds favorable to the durability of the pvr2-mediated resistance were carried by genetically distant landraces from diversified origins, indicating that such favorable genetic combinations are not only frequent but also widespread in the pepper genetic resources. The relationship between the pvr2 3/4 RB frequency and the level of quantitative resistance in a diversified core-collection extends the previous results which showed that the RB frequency of a major gene is reduced when introgressed into a partially

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resistant cultivar (Palloix et al., 2009;[START_REF] Brun | Quantitative resistance increases the durability of qualitative resistance to Leptosphaeria maculans in Brassica napus[END_REF][START_REF] Fournet | Selection of nematodes by resistant plants has implications for local adaptation and crossvirulence[END_REF] or combined with another major resistance gene (Acosta-Leal andXiong 2008, 2013), and that the same QTLs or genes may affect quantitative resistance and major gene durability [START_REF] Acosta-Leal | Complementary functions of two recessive R-genes determine resistance durability of tobacco 'Virgin A Mutant' (VAM) to Potato virus Y[END_REF]Quenouille et al 2014). This former QTL analysis, together with the analysis of the eIFiso4E coding sequence in the core collection leads us to suggest that observed variations of RB frequency are strongly affected by the plant allele at the pvr6 locus.

However, the genetic background effect cannot be reduced to this single locus since this major effect can be compensated by additional quantitative resistance QTLs. This indicates that breeding "accidents" could happen when a major resistance gene is introgressed into a new genetic background. However, such accidents can be avoided if the major resistance gene is introgressed into a partially resistant cultivar, taking into account that quantitative resistance has to be evaluated through pathogen accumulation level since the symptom expression or

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Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury resistance breakdown events associated to the selection of the aspartic acid to asparagine substitution at codon position 119 of PVY VPg cistron (VPg-N mutation).

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Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury

  , B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277

  , B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277

  , B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277

  conferred by the genetic background (Quenouille et al. 2014). To explore this relationship in an enlarged germplasm, we estimated the level of quantitative resistance conferred by the genetic backgrounds of each of the 20 pepper accessions. The pvr2 3/4 -breaking mutant of the CI chimera carrying the VPg-N mutation was inoculated to 20 plants per accession. This RB mutant was chosen because it was the most frequently observed after RB of the pvr2 3 resistance by the CI chimera. It differed from the CI chimera by only one amino acid substitution (aspartic acid to asparagine) at position 119 of the VPg, allowing the breakdown Accepted Article Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury, B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277This article is protected by copyright. All rights reserved.of pvr2 3 and pvr2 4 and permitting to get rid of the effect of the pvr2-mediated resistance in order to reveal the effect of the genetic background. Symptoms were assessed every seven days until 35 dpi and for each plant the Area Under the Disease Progress Curve (AUDPC)was calculated according to[START_REF] Caranta | Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y[END_REF]: symptom intensity from each plant was checked on the new developping leaves, with 0 (no symptom), 1 (weak mosaic) or 2 (severe mosaic or necrosis) at 7, 14,21, 28 and 35 dpi. At 36 dpi, the relative virus accumulation (VA) was evaluated independently from 10 plants per accession by quantitative DAS-ELISA by comparing the absorbance at 405 nmdilution factor curves of each plant sample to that of a common reference virus sample (Ayme et al. 2006). Significant differences of VA and AUDPC were observed between accessions (p<0.001, Kruskal-Wallis test) with means of VA varying from 0.001 to 2.804 and means of AUPDC varying from 35 to 95 (table 1). Nine and eight groups of VA and AUDPC, respectively, were identified among the 20 peppers accessions (pairwise comparisons using Wilcoxon tests at 5% type-I error threshold after Benjamini & Yekutieli correction), showing a large diversity of the level of quantitative resistance conferred by the accession's genetic backgrounds. No significant correlation was observed between VA and AUDPC (p=0.3, Spearman correlation test). This lack of correlation between VA and AUDPC (or plant damages) was previously observed for different plant-virus interactions (Sáenz

  , B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277

  , B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277

  tolerance level was not correlated to resistance breakdown frequency. Another interesting output was delivered by the distribution of the different RB mutants which differed between pepper landraces, suggesting that selection pressures could be modulated thanks to different plant genetic backgrounds. The availability of plant genetic backgrounds with contrasted differential effects on pathogen populations paves the way towards a durable management of resistance genes by breeding appropriate cultivars and deploying appropriate varietal mixtures to control the emergence of the different RB variants. Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury, B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277 This article is protected by copyright. All rights reserved. d'Azur (PACA) and the INRA-Meta Programme SMaCH (Sustainable Management of Crop Health).

  , B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277This article is protected by copyright. All rights reserved.

  Figure legends:

  , B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277 This article is protected by copyright. All rights reserved. Mundt, C., Cowger, C. and Garrett, K. (2002). Relevance of integrated disease management to resistance durability. Euphytica 124: 245-252. Nicolaï M., Cantet M., Lefebvre V., Sage-Palloix A.M., Palloix A. (2013). Genotyping a large collection of pepper (Capsicum spp) with SSR loci brings new evidence for the wild origin of cultivated C. annuum and the structuring of genetic diversity by human selection of cultivar types. Genetic Resources and Crop Evolution, 60:2375-2390. Pagán, I., Alonso-Blanco, C. and García-Arenal, F. (2007). The relationship of within-host multiplication and virulence in a plant-virus system. PLoS ONE 2: e786. Palloix, A., Ayme, V. and Moury, B. (2009). Durability of plant major resistance genes to pathogens depends on the genetic background, experimental evidence and consequences for breeding strategies. New Phytologist 183: 190-199. Perrier, X., Jacquemoud-Collet, J.P.(2006). DARwin software http://darwin.cirad.fr/ Pink D. (2002). Strategies using genes for non-durable disease resistance. Euphytica 124: 227-236. Quenouille, J., Montarry, J., Palloix, A. and Moury B. (2012). Farther, slower, stronger: how the plant genetic background protects a major resistance gene from breakdown. Molecular Plant Pathology: 14: 109-118. Quenouille, J., Paulhiac, E., Moury, B., Palloix, A. (2014). Quantitative trait loci from the host genetic background modulates the durability of a resistance gene: a rational basis for sustainable resistance breeding in plants. Heredity, 112: 579-587. Råberg, L., Sim, D., and Read, A. F. (2007). Disentangling genetic variation for resistance and tolerance to infectious diseases in animals. Science 318: 812-814. translation initiation factors eIF4E and eIF(iso)4E are required to prevent pepper veinal mottle virus infection of pepper. J Gen Virol 87: 2089-2098. Accepted Article Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury, B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277 This article is protected by copyright. All rights reserved. 2000). Identification of a pathogenicity determinant of Plum pox virus in the sequence encoding the C-terminal region of protein P3+ 6K1. Journal of General Virology 81: in pepper genetic resources: distribution of horticultural and resistance traits in the inra pepper germplasm. In Progress in research on Capsicum & Eggplant. Niemirowicz-Szczytt K. (Ed.), University of Life Sciences Press, Warsaw, Poland, pp.33:42. Wolfe, M. (1985). The current status and prospects of multiline cultivars and variety mixtures for disease resistance. Annual Review of Phytopathology 23: 251-273. Accepted Article Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury, B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277 This article is protected by copyright. All rights reserved. MPP_12277_F1 Accepted Article Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury, B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277 This article is protected by copyright. All rights reserved. Accepted Article Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury, B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277This article is protected by copyright. All rights reserved.

  The 20 accessions represented 36.7% of the allelic richness present in the entire C. annuum collection (mean of 4.6 alleles for the 20 accessions compared to 12.6 alleles for the whole C.annuum collection at the 28 SSR loci, Nicolaï et al., 2013). These results indicate that, in spite of the choice based on two related pvr2 alleles, the retained 20 accessions carried diverse genetic backgrounds.

  , so that Perennial always displayed an extremely low (or null) RB frequency.Compared to the Yolo Wonder pvr6 + allele, the pvr6 allele of Perennial carries a 82 nucleotide deletion (from nucleotide 89 to 170) which modifies the open reading frame (ORF), leading to a premature stop codon and a truncated, nonfunctional protein(Ruffel et al. 2006). To explore if this "natural" knockout (KO) of the pvr6 allele was present among the 20 pepper accessions and if it was associated to the observed variations of VA and pvr2 3/4 RB frequency, we sequenced the eIFiso4E cDNA of the 20 pepper accessions as described inRuffel et al. (2006). These sequences were aligned with the sequences of the Yolo Wonder pvr6 (2014) showed that in Perennial the effect of the QTL allele at the pvr6 locus was compensated by three other QTLs that decreased the pvr2 3 RB frequency and virus accumulation. Taken together, these results show that the pvr6 gene is a good candidate to explain the observed variation of pvr2 RB frequency and VA. The high frequency of pvr2 3/4 RB observed in G4 and PI369940 could be interpreted as an effect of the pvr6 KO allele which increased both VA and RB

, B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277

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background+ allele (Genbank accession DQ022080) and the Perennial pvr6 allele (Genbank accession DQ022083).described in

Ruffel et al. (2006)

. Alleles of the pvr6 gene carried by each pepper accession are indicated in Table

2

. Among the 20 pepper accessions, three carried the same KO pvr6 allele: Perennial, PI369940 and G4. Interestingly, the two accessions PI369940 and G4 which showed a significantly higher RB frequency of pvr2 3/4 and the two highest VA values carried the KO pvr6 allele. On the opposite, all plants carrying the pvr6 + allele encoding a functional eIF(iso)4E protein displayed a low to very low RB frequency and a varying but lower VA. The pvr6 allele is also present in the Perennial accession, which showed a very low RB frequency and this could invalidate the causal relationship between pvr6 alleles and both RB frequency and VA. However, Quenouille et al.

frequencies, without compensation effects from other QTLs in the genetic background as observed in Perennial. This simultaneous increase of VA and RB may result from a higher

Accepted Article

Comment citer ce document : Quenouille, J., Saint-Félix, L.,

Moury

, B. (Auteur de correspondance), Palloix, A. (2016). Diversity of genetic backgrounds modulating the durability of a major resistance gene. Analysis of a core collection of pepper landraces resistant to Potato virus Y. Molecular Plant Pathology, 17 (2), 296-302. DOI : 10.1111/mpp.12277

This article is protected by copyright. All rights reserved.

Table legends :

 legends Table 1 : Frequency of resistance breakdown (RB), relative viral accumulation (VA) and area under the disease progress curve (AUDPC) for 20 pepper accessions carrying the pvr2

				3	or
	pvr2	4	allele inoculated with Potato virus Y.
	w	Letters represent homogeneous groups identified by pairwise comparisons (Fisher exact tests at the
	5% type-I error threshold corresponding to a 0.00027 threshold after Bonferroni correction for
	multiple comparisons). RB frequency evaluated after inoculation with PVY CI chimera.
	x	Letters represent homogeneous groups identified by pairwise comparisons (Wilcoxon tests at the 5%
	type-I error threshold with Benjamini & Yekutieli correction). VA and AUSPC evaluated after
	inoculation with PVY CI chimera carrying the VPg-N mutation.
	y	In three accessions a 82 nucleotide (nt) deletion (from nucleotide 89 to 170) resulted in a premature
	stop codon and a truncated nonfunctional eIFiso4E (Ruffel et al. 2006).
	Table 2: Frequency of pvr2	3/4

Table 2

 2

	Accession PI369940 G4 DH285 Accepted Article	% of plants with VPg-N mutation 29 (7/24) 55 (17/31) 60 (16/25)	Class a a ab b

Acknowledgements

The authors thank G. Nemouchi, and V. Simon for technical assistance, A.M. Sage-Palloix (CRB-Leg, INRA-GAFL) for providing the Capsicum genetic resources. This work was supported by Gautier-Semences and financially funded by the Agence Nationale de la Recherche (Project VirAphid ANR-2010STRA-001-01), the Région Provence Alpes Côte Accepted Article

Comment citer ce document : Quenouille, J., Saint-Félix, L., Moury


Klaus M Frahm
email: frahm@irsamc.ups-tlse.fr

Samer El Zant
email: samer.elzant@enseeiht.fr

Katia Jaffrès-Runser

Dima L Shepelyansky

Multi-cultural Wikipedia mining of geopolitics interactions leveraging reduced Google matrix analysis

Keywords:

Geopolitical interactions of countries

Geopolitics focuses on political power in relation to geographic space. Interactions among world countries have been widely studied at various scales, observing economic exchanges, world history or international politics among others. This work exhibits the potential of Wikipedia mining for such studies. Indeed, Wikipedia stores valuable fine-grained dependencies among countries by linking webpages together for diverse types of interactions (not only related to economical, political or historical facts). We mine herein the Wikipedia networks of several language editions using the recently proposed method of reduced Google matrix analysis. This approach allows to establish direct and hidden links between a subset of nodes that belong to a much larger directed network. Our study concentrates on 40 major countries chosen worldwide. Our aim is to offer a multicultural perspective on their interactions by comparing networks extracted from five different Wikipedia language editions, emphasizing English, Russian and Arabic ones. We demonstrate that this approach allows to recover meaningful direct and hidden links among the 40 countries of interest.

Introduction

Political and economic interactions between regions of the world have always been of utmost interest to measure and predict their relative influence. Such studies belong to the field of geopolitics that focuses on political power in relation to geographic space. Interactions among world countries have been widely studied at various scales (worldwide, continental or regional) using different types of information. Studies are driven by observing economic exchanges, social changes, history, international politics and diplomacy among others [START_REF] Jones | The European Miracle: Environments, Economies and Geopolitics in the History of Europe and Asia[END_REF][START_REF] Dittmer | Popular geopolitics past and future: fandom, identities and audiences[END_REF]. The major finding of this paper is to show that meaningful worldwide interactions can be automatically extracted from the global and free online Encyclopaedia Wikipedia [3] for a given set of countries. All information gathered in this collaborative knowledge base can be leveraged to provide a picture of countries relationships, fostering a new framework for thorough geopolitics studies.

Wikipedia has become the largest open source of knowledge being close to Encyclopaedia Britannica [4] by the accuracy of its scientific entries [5] and overcoming the latter by the enormous quantity of available information. A detailed analysis of strong and weak features of Wikipedia is given at [START_REF] Reagle | Good Faith Collaboration: The Culture of Wikipedia[END_REF][START_REF] Nielsen | Wikipedia research and tools: review and comments[END_REF]. Wikipedia articles make citations to each other, providing a direct relationship between webpages and topics. As such, Wikipedia generates a larger directed network of article titles with a rather clear meaning. For these reasons, it is interesting to apply algorithms developed for search engines of World Wide Web (WWW) such as the PageRank algorithm [START_REF] Brin | [END_REF] (see also [START_REF] Langville | Google's PageRank and Beyond: The Science of Search Engine Rankings[END_REF]), to analyze the ranking properties and relations between Wikipedia articles. For various language editions of Wikipedia it was shown that the PageRank vector produces a reliable ranking of historical figures over 35 centuries of human history [START_REF] Zhirov | [END_REF][11][12][13][14] and a solid Wikipedia ranking of world universities (WRWU) [START_REF] Zhirov | [END_REF]15]. It has been shown that the Wikipedia ranking of historical figures is in a good agreement with the well-known Hart ranking [START_REF] Hart | The 100: Ranking of the Most Influential Persons in History[END_REF], while the WRWU is in a good agreement with the Shanghai Academic ranking of world universities [START_REF]Academic ranking of world universities[END_REF].

At present directed networks of real systems can be very large (about 4.2 million articles for the English Wikipedia edition in 2013 [13] or 3.5 billion web pages (called also nodes) for a publicly accessible web crawl that was gathered by the Common Crawl Foundation in 2012 [START_REF] Meusel | [END_REF]). For some studies, one might be interested only in the particular interactions between a very small subset of nodes compared to the full network size. For instance, in Fig. 1. Geographical distribution of the 40 selected countries. Color code groups countries into 7 sets: orange (OC) for English speaking countries, blue (BC) for former Soviet union ones, red (RC) for European ones, green (GC) for Latin American ones, yellow (YC) for Middle Eastern ones, purple (PUC) for North-East Asian ones and finally pink (PIC) for South-Eastern countries (see colors and country names in Table 1; other countries are shown in black). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) this paper, we are interested in capturing the interactions of the 40 countries represented in Fig. 1 using the networks extracted from five Wikipedia language editions covering a few millions of articles each. However, let us assume that there is a rather important person (having his own Wikipedia article corresponding to a node C ) who was born in country A and worked the main part of his life in country B; therefore A and B may have links to C (in either direction) and thus there may be an indirect link between the two nodes A and B via the node C (or other nodes). In previous works, a solution to this general problem has been proposed in [19,20] by defining the reduced Google matrix theory. Main elements of Reduced Google matrix G R will be presented next, but in a few words, it captures in a 40-by-40 Perron-Frobenius matrix the full contribution of direct and indirect interactions happening in the full Google matrix between the 40 nodes of interest (we took top 40 countries of PageRank vector of EnWiki). Elements of reduced matrix G R (i, j) can be interpreted as the probability for a random surfer starting at webpage j to arrive in webpage i using direct and indirect interactions. Indirect interactions refer to paths composed in part of webpages different from the 40 ones of interest. Even more interesting and unique to reduced Google matrix theory, we show here that intermediate computation steps of G R offer a decomposition of G R into matrices that clearly distinguish direct from indirect interactions. As such, it is possible to extract the probability for an indirect interaction between two nodes to happen.

Reduced Google matrix theory is a perfect candidate for analyzing the direct and indirect interactions between countries selected worldwide. In this paper, we extract from G R and its decomposition into direct and indirect matrices of selected subset network of N r = 40 countries. The Google matrix of this subset network of N r nodes is computed taking into account direct and hidden (i.e. indirect) directed links. More specifically, we deduce a finegrained classification of countries that captures what we call the hidden friends and hidden followers of a given country. The structure of these graphs provides relevant social information: communities of countries with strong ties can be clearly exhibited while countries acting as bridges are present as well. This is mainly the case for the hidden interactions networks of friends (or followers) that offer new information compared to the direct networks of friends (or followers) whose topology is mainly enforced by top PageRank countries. The mathematical procedure of the reduced G R matrix construction for N r nodes is described in detail in Section 2.

The networks of G R direct and hidden interactions can be calculated for different Wikipedia language editions. In this paper, reduced Google matrix analysis is applied to the same set of 40 countries on networks representing five different Wikipedia editions: English (EnWiki), Arabic (ArWiki), Russian (RuWiki), French (FrWiki) and German (DeWiki) editions. We take for analysis the top 40 countries according to the EnWiki PageRank. Wikipedia language editions are usually modified by authors who mainly belong to the region associated with this language. Thus our study shows the impact of this cultural bias when comparing direct and hidden networks of friends (or followers) among different language editions. We show that part of the interactions are crosscultural while others are clearly biased by the culture of the authors.

In Section 2 we introduce the main elements of reduced Google matrix theory, Section 3 describes G R calculated for 40 countries and for five different Wikipedia editions. Specific emphasis is given to the very different English, Arabic and Russian editions. Networks of friends and followers for direct and hidden interaction matrices are created and discussed in Section 4, and conclusion is drawn in Section 5.

Reduced Google matrix theory

Google matrix

It is convenient to describe the network of N Wikipedia articles: a network node is given by the article name, all nodes are numbered, some nodes correspond to articles with country names, see Table 1; the number of countries is much smaller than the total number of articles N. Then the Google matrix Gis constructed from the adjacency matrix A ij with elements 1 if article (node) j points to article (node) i and zero otherwise. In this case, elements of the Google matrix take the standard form [START_REF] Brin | [END_REF][START_REF] Langville | Google's PageRank and Beyond: The Science of Search Engine Rankings[END_REF]

G ij = α S ij + (1 -α)/N , ( 1
)
where S is the matrix of Markov transitions with elements

S ij = A ij /k out ( j), k out ( j) = N
i=1 A ij = 0 being the node j out-degree (number of outgoing links) and with S ij = 1/N if j has no outgoing links (dangling node). Here 0 < α < 1 is the damping factor which for a random surfer determines the probability (1α) to jump to any node; below we use α = 0.85. The right eigenvectors ψ i ( j) of G are defined by:

j G jj ψ i ( j ) = λ i ψ i ( j) .
(2)

The PageRank eigenvector P ( j) = ψ i=0 ( j) corresponds to the largest eigenvalue λ i=0 = 1 [START_REF] Brin | [END_REF][START_REF] Langville | Google's PageRank and Beyond: The Science of Search Engine Rankings[END_REF]. It has positive elements which give the probability to find a random surfer on a given node in the stationary long time limit of the Markov process. All nodes can be ordered by a monotonically decreasing probability P (K i ) with the highest probability at K = 1. The index K is the PageRank index. The PageRank vector is computed by the PageRank algorithm with iterative multiplication of initial random vector by G matrix [START_REF] Brin | [END_REF][START_REF] Langville | Google's PageRank and Beyond: The Science of Search Engine Rankings[END_REF]14]. Left eigenvectors are biorthogonal to right eigenvectors of different eigenvalues. The left eigenvector for λ = 1 has identical (unit) entries due to the column sum normalization of G. In the following we use the notations ψ T L and ψ R for left and right eigenvectors, respectively. Notation T stands for vector or matrix transposition.

In addition to the matrix G it is useful to introduce a Google matrix G * constructed from the adjacency matrix of the same network but with inverted direction of all links [21]. The vector P * (K * ) is called the CheiRank vector [START_REF] Zhirov | [END_REF]21] and the index numbering nodes in order of monotonic decrease of probability P * is noted as CheiRank index K * . Thus, nodes with many ingoing (or outgoing) links have small values of K = 1, 2, 3... (or of K * = 1, 2, 3, ...) [START_REF] Langville | Google's PageRank and Beyond: The Science of Search Engine Rankings[END_REF]14]. We show the distribution of selected countries on the PageRank-ChiRank plane (K , K * ) in Fig. 2.

Reduced Google matrix

We construct the reduced Google matrix for a certain subset of N r selected nodes from the global Wikipedia network with N nodes (N r N). As a subset we choose top 40 countries with the largest PageRank probabilities for EnWiki network (the names are given in Table 1). The reduced Google matrix G R is constructed on the mathematical basis described below. The main element of this construction is to keep the same PageRank probabilities of N r nodes as in the global network (up to a fixed multiplier coefficient) and to take into account all indirect links between N r nodes coupled by transitions via N -N r nodes of the global network (see also [20]).

Let G be a typical Google matrix (1) for a network with N nodes such that G ij ≥ 0 and the column sum normalization

N i=1 G ij = 1 is verified.
We consider a sub-network with N r < N nodes, called "reduced network". In this case we can write G in a block form:

G = G rr G rs G sr G ss (3)
where the index "r" refers to the nodes of the reduced network and "s" to the other N s = N -N r nodes which form a complementary network which we will call the "scattering network". Thus G rr is given by the direct links between selected N r nodes, G ss describes links between all other N -N r nodes, G rs and G sr give links between these two parts. PageRank vector of the full network is given by:

P = P r P s (4)
which satisfies the equation G P = P or in other words P is the right eigenvector of G for the unit eigenvalue. This eigenvalue equation reads in block notations:

(1

-G rr ) P r -G rs P s = 0, (5)
-

G sr P r + (1 -G ss ) P s = 0. ( 6
)
Here 1 is the unit matrix of corresponding size N r or N s . Assuming that the matrix 1 -G ss is not singular, i.e. all eigenvalues G ss are strictly smaller than unity (in modulus), we obtain from (6) that

P s = (1 -G ss ) -1 G sr P r ( 7
)
which gives together with (5): [START_REF] Brin | [END_REF] where the matrix G R of size N r × N r , defined for the reduced network, can be viewed as an effective reduced Google matrix. Here the contribution of G rr accounts for direct links in the reduced network and the second matrix inverse term corresponds to all contributions of indirect links of arbitrary order. The matrix elements of G R are non-negative since the matrix inverse in (8) can be expanded as:

G R P r = P r , G R = G rr + G rs (1 -G ss ) -1 G sr
(1

-G ss ) -1 = ∞ l=0 G l ss . ( 9
)
In ( 9) the integer l represents the order of indirect links, i.e. the number of indirect links which are used to connect indirectly two nodes of the reduced network. We refer the reader to [20] to get the proof that G R also fulfills the condition of column sum normalization being unity.

Numerical evaluation of G R

We can question how to evaluate practically the expression [START_REF] Brin | [END_REF] of G R for a particular sparse and quite large network when N r ∼ 10 2 -10 3 is small compared to N and N s ≈ N N r . If N s is too large (e.g. N s > 10 5 ) a direct naive evaluation of the matrix inverse (1 -G ss ) -1 in ( 8) by Gauss algorithm is not efficient. In this case we can try the expansion (9) provided it converges sufficiently fast with a modest number of terms. However, this is most likely not the case for typical applications since G ss is very likely to have at least one eigenvalue very close to unity. Therefore, we consider the situation where the full Google matrix has a well defined gap between the leading unit eigenvalue and the second largest eigenvalue (in modulus). For example if G is defined using a damping factor α in the standard way, as in (1), the gap is at least 1α which is 0.15 for the standard choice α = 0.85 [START_REF] Langville | Google's PageRank and Beyond: The Science of Search Engine Rankings[END_REF]. In order to evaluate the expansion (9) efficiently, we need to take out analytically the contribution of the leading eigenvalue of G ss close to unity which is responsible for the slow convergence.

Below we denote by λ c this leading eigenvalue of G ss and by ψ R (ψ T L ) the corresponding right (left) eigenvector such that

G ss ψ R = λ c ψ R (or ψ T L G ss = λ c ψ T L ).
Both left and right eigenvectors as well as λ c can be efficiently computed by the power iteration method in a similar way as the standard PageRank method. Vectors ψ R are normalized with E T s ψ R = 1 and ψ L with ψ T L ψ R = 1. It is well known (and easy to show) that ψ T L is orthogonal to all other right eigenvectors (and ψ R is orthogonal to all other left eigenvectors) of G ss with eigenvalues different from λ c . We introduce the operator P c = ψ R ψ T L which is the projector onto the eigenspace of λ c and we denote by Q c = 1 -P c the complementary projector.

One verifies directly that both projectors commute with the matrix G ss and in particular P c G ss = G ss P c = λ c P c . Therefore we can derive:

(1

-G ss ) -1 = P c 1 1 -λ c + Q c ∞ l=0 Ḡ l ss ( 10
)
with Ḡss = Q c G ss Q c and using the standard identity P c Q c = 0 for complementary projectors. The expansion in [START_REF] Zhirov | [END_REF] converges rapidly since Ḡ l ss ∼ |λ c,2 | l with λ c,2 being the second largest eigenvalue which is significantly lower than unity. The combination of ( 8) and ( 10) provides an explicit algorithm feasible for a numerical implementation for modest values of N r , large values of N s and of course if sparse matrices G, G ss are considered. We refer the reader to [20] for more advanced implementation considerations.

Decomposition of G R

On the basis of equations ( 8)- [START_REF] Zhirov | [END_REF], the reduced Google matrix can be presented as a sum of three components: (11) with the first component G rr given by direct matrix elements of G among the selected N r nodes. The second projector component G pr is given by:

G R = G rr + G pr + G qr ,
G pr = G rs P c G sr /(1 -λ c ), P c = ψ R ψ T L . ( 12
)
The third component G qr is of particular interest in this study as it characterizes the impact of indirect or hidden links. It is given by:

G qr = G rs [Q c ∞ l=0 Ḡ l ss ]G sr , Q c = 1 -P c , Ḡss = Q c G ss Q c . ( 13
)
We do characterize the strength of these 3 components by their respective weights W rr , W pr , W qr given respectively by the sum of all matrix elements of G rr , G pr , G qr divided by N r . By definition we have W rr + W pr + W qr = 1.

Reduced Google matrix has been computed, together with its components G rr , G pr and G qr , for the English language edition of Wikipedia (EnWiki) and for the N R = 40 countries listed in Table 1. These countries are the ones with top PageRank K in the network of EnWiki. Density plots of G R , G rr , G pr and G qr , are given in Fig. 3. Countries are ordered by increasing K value. The weight of the three matrix components of G R are W pr = 0.96120, W qr = 0.029702 and W rr = 0.009098. Predominant component is clearly G pr but as we will explain next, it is not the most meaningful.

The meaning of G rr is clear as it is directly extracted from the global Google matrix G. It gives the direct links between the selected nodes and more specifically the probability G rr (i, j) for the surfer to go directly from column j country to line i country. However, since each column is normalized by the number of outgoing links, absolute probabilities cannot be compared to each other across columns.

The sum of G pr and G qr represents the contribution of all indirect links through the scattering matrix G ss . As seen on Fig. 3, the projector component G pr is composed of nearly identical columns. Moreover, values of each column are proportional to the PageRank of the countries (lines and columns are ordered by increasing K values). As detailed in [20], we observe numerically that G pr ≈ P r E T r /(1λ c ), meaning that each column is close to the normalized vector P r /(1λ c ). As such, G pr transposes essentially in G R the contribution of the first eigenvector of G. We can conclude that even if the overall column sums of G pr account for ∼95-97% of the total column sum of G R , G pr doesn't offer innovative information compared to PageRank analysis.

A way more interesting contribution is the one of G qr . This matrix captures higher-order indirect links between the N r nodes due to their interactions with the global network environment. We will refer to these links as hidden links. We note that G qr is composed of two parts G qr = G qrd + G qrnd where the first term gives only the diagonal part of the matrix G qrd and thus represents the probabilities to stay on the same node during multiple iterations of Ḡss in (13) while the second matrix captures only non-diagonal terms in G qrnd . As such, G qrnd represents indirect (hidden) links between the N r nodes appearing via the global network. We note that certain matrix elements of G qr can be negative, which is possible due to the negative terms in Q c = 1 -P c appearing in (13). The total weight of negative elements is however much smaller than W qr (at least 6 times smaller and even non-existing in ArWiki). Of course, the full reduced Google matrix G R has only positive or zero matrix elements. In the following, our study concentrates mainly on the meaning of G qrnd , emphasizing the meaning of its largest positive values in the study of Section 4.

Matrices of world countries

Our study focuses on the networks representing 5 different Wikipedia editions 1 from the set of 24 analyzed in [13]: EnWiki, ArWiki, RuWiki, DeWiki and FrWiki that contain 4.212, 0.203, 0.966, 1.533 and 1.353 million of articles each.

Selected countries

The 40 countries listed in Table 1 have been selected from the EnWiki network after computing the PageRank for the complete network. The 40 countries with largest PageRank probability have been chosen, and ordered by a local PageRank index K varying between 1 and 40. The most influential countries are found to be at the top values K = 1, 2, .... In addition we determine the local CheiRank index K * of the selected countries using the CheiRank vector of the global network [14,21]. At the top of K * we have the most communicative countries. Table 1 lists K and K * for EnWiki, ArWiki and RuWiki. Not surprisingly, the order of top countries changes with respect to the edition (for instance, the top country for K is US except for RuWiki whose top country is Russia).

Countries that belong to the same region or having a common piece of history may probably exhibit stronger interactions in Wikipedia. As such, we have created a color code that groups together countries that either belong to the same geographical 1 Data collected mid February 2013.

region (e.g. Europe, Latin America, Middle East, North-East Asia, South-East Asia) or share a big part of history (former USSR; English speaking countries that are the legacy of the former British Empire). Color code can be seen either in Fig. 1 or in the text color of Table 1.

It is convenient as well to plot all nodes in the (K , K * ) plane to highlight the countries that are the most influential (K = 1, 2, ...) and the most communicative (K * = 1, 2, ...) at the same time.

Fig. 2 plots all 40 countries in the (K , K * ) plane for EnWiki, ArWiki and RuWiki editions. This plot is a bi-objective plot where K and K * are to be minimized concurrently. It is interesting to look at the set of non-dominated countries which are the ones such that there is no other country beating them for both K and K * . Cultural bias is obvious here as for EnWiki, this set is composed of {US, JP, IR, AR}, for ArWiki of {US, EG, IT} and for RuWiki of only Russia. We note that according to Fig. 2 some countries with high K value (relative few in-degree and low PageRank probability) act as important diffusers of content (low K * ) even for the language editions being different from the language spoken in those countries (BR, AR, RO). Also countries with low K (having many citations) are relatively poor diffusers (FR, CA). Thus Fig. 2 demonstrates that different cultures attribute different degree of country popularity (PageRank probability and K index) and different communicative degree (CheiRank probability and K * index). This indicates the nontrivial features of cultures propagation and interactions.

Density plots of G R , G rr and G qrnd

For the three EnWiki, ArWiki and RuWiki editions, Fig. 4 plots the density of matrices G R , G qrnd and G rr . We keep for all plots the same order of countries extracted from the EnWiki network. This is meant to highlight cultural differences among Wikipedia editions. In the G R plots, it is clear that this matrix is dominated by the projector G pr contribution, which is proportional to the global PageRank probabilities. In G R , not surprisingly, the cultural bias is pronounced due to its strong tie to PageRank. For instance, Egypt is much more important in ArWiki than in other editions, and Russia is the top country in RuWiki.

The information from direct links between countries is provided by G rr . As expected, the per-column normalization prevents a meaningful per-line analysis. For EnWiki and ArWiki, the respective columns of Mexico and Hungary are predominant due to their little number of outgoing links. On the contrary, G qrnd offers a much more unified view of countries interactions as it seems to highlight more general interaction that are less biased by cultural views. For instance, for these three Wikipedia editions, the hidden links connecting Taiwan to China and Pakistan to India are really strong in G qrnd . The link connecting Ukraine to Russia is very strong in EnWiki and ArWiki. It is surprisingly absent from RuWiki (or maybe this is exactly a cultural bias we are observing since during a long time both countries were part of USSR, and there was thus no specific difference between them). Other interesting hidden links are highlighted in EnWiki as New-Zealand is directed to Australia or in RuWiki linking Canada to the USA.

Friends and followers

In order to better capture the interactions provided by G qrnd and G R , we have listed for all 5 Wikipedia editions the top 4 friends and top 4 followers of a set of 7 leading countries. One leading country per group has been selected: US for English speaking countries, Brazil for Latin America, France for Europe, Japan for North-East Asia, India for South-East Asia, Russia for the Soviet block and Turkey for the Middle-East. To pick them inside each group, we have chosen the country whose worst PageRank order over all 5 Wikipedia editions is the highest. For each leading country, we extract from both matrices G qrnd and G R the top 4 Friends (resp. Followers) of country j given by the 4 best values of the elements of column j (resp. of line j).

In other words, it corresponds to destinations of the 4 strongest outgoing links of j and the countries at the origin of strongest 4 ingoing links. A summary of relevant results is given in Table 2 to show cross-culture interactions.

Looking at G R friends, top friends of leading countries are strongly related to the top PageRank countries (we have a predominance of US, France and Germany). Similarly, cross-edition followers of US are Mexico and Canada, and followers of Japan are China, Korea and Taiwan. On the opposite, higher-order interactions of G qrnd are not as much influenced by PageRank. More subtle but realistic interactions appear: Canada is always identified as a hidden friend of USA while it was never the case in G R . Similarly, Ukraine is always tagged as a hidden friend of Russia; Italy and Spain as friends of France. Thus G qrnd seems to emphasize more fine-grained regional interactions. Next section exploits the concept of friends and followers to create new network representations derived from G R and G qrnd .

Networks of 40 countries

This study concentrates again on the same 7 leading countries as before. Top 4 friends and top 4 followers of these leading countries are extracted from G R and G qrnd to plot the graphs of Figs. 5 and 6, respectively. Note that Fig. 6 essentially highlights hidden links. The black thick arrows identify the top 4 friends and top 4 followers interactions. Red arrows represent the friends of friends (respectively the followers of followers) interactions that are computed recursively until no new edge is added to the graph. All graphs are plotted using a force direct layout. The networks of friends obtained from G R never expand to the full set of 40 nodes. They only concentrate on about 10 countries (including the 7 leading ones). This happens since G R is dominated by the projector component. Looking at the follower graphs, more information can be observed. North-East Asian, Middle-Eastern and Latin American create, in all editions, a cluster of nodes densely interconnected. European countries enclose Russia and Ukraine as these countries are linked to EU countries that were part of the former Soviet Union zone of influence (e.g. Romania, Hungary, Finland, etc.). The networks of followers end up almost spanning the full set of 40 countries.

The networks of friends obtained from G qrnd don't concentrate to a limited set of countries as it is the case for G R . They end up spanning the full set of countries. The hidden friend links show that the interactions between the geographical groups are coherent. North-East Asian countries are linked to South-East Asian countries and to English speaking countries in EnWiki and RuWiki. Interestingly, the set of Baltic countries (SE, NO, DK, FI) create most of the time full meshes, and interconnect Europe and Russia. Cultural bias can be observed as well in these plots. For non-Arabic editions, Middle-Eastern countries create a well-connected cluster of nodes. But for ArWiki, Turkey exhibits a stronger connection with Europe than with the other Middle-Eastern countries. In the view of Arabic countries, Turkey is seen closer to Europe than others for sure.

Conclusion

This work offers a new perspective for future geopolitics studies. It is possible to extract from multi-cultural Wikipedia networks a global understanding of the interactions between countries at a global, continental or regional scale. On the basis of the reduced Google matrix analysis of the Wikipedia network we determined the relations of friends and followers of countries on purely statistical mathematical grounds obtained from the huge knowledge accumulated by Wikipedia editions in different languages. This approach provides results independent of cultural bias. The reduced Google matrix theory has been shown to capture hidden and indirect interactions among countries, resulting in new knowledge on geopolitics.

Fig. 2 .

 2 Fig. 2. Position of countries in the local (K , K * ) plane of the reduced network of 40 countries in the EnWiki (left), ArWiki (middle) and RuWiki (right) networks.

Fig. 3 .

 3 Fig. 3. Density plots of matrices G R (top left), G pr (top right), G rr (bottom left) and G qr (bottom right) for the reduced network of 40 countries in the EnWiki network. The nodes N r are ordered in lines by increasing PageRank index (left to right) and in columns by increasing PageRank index from top to bottom. Color scale represents maximum values in red (0.15 in top panels; 0.01 in bottom left panel; 0.03 in bottom right panel), intermediate in green and minimum (approximately zero) in blue. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4 .

 4 Fig. 4. Density plots of the matrix elements of G R (first line), G qrnd (second line) and G rr (third line) for the reduced network of 40 countries of EnWiki (left column), ArWiki (middle column) and RuWiki (right column). The country names are given on the axes in the order names in Table 1, thus the nodes N r are ordered in lines and columns by the reference PageRank of EnWiki. The colors represent maximum (red corresponds to: 0.15, 0.19, 0.13 in top panels from left to right; 0.01, 0.03, 0.012 in middle panels and 0.01, 0.011, 0.006 in bottom panels respectively), intermediate (green) and minimum (blue for zero) values for a given matrix. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 .Fig. 6 .

 56 Fig. 5. Network structure of friends (top line) and followers (bottom line) induced by the 7 top countries of each geographical area (US, FR, IN, JP, BR, TR, RU) in G R . Results are plotted for EnWiki (left column), ArWiki (middle column) and RuWiki (right column). Node colors represent geographic appartenance to a group of countries (cf. Table1for details). Top (bottom) graphs: the top country node points (is pointed by) with a bold black arrow to its top 4 friends (followers). Red arrows show friends of friends (resp. followers of followers) interactions computed until no new edges are added to the graph. Drawn with[START_REF] Bastian | Gephi: an open source software for exploring and manipulating networks[END_REF]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1

 1 List of names of 40 selected countries with PageRank K , CheiRank K * for EnWiki, ArWiki and RuWiki, ordered by increasing PageRank of EnWiki edition. Fig.1gives color correspondence details. A Wikipedia article with country name represents one node of the whole network with N nodes, e.g. https :/ /en .wikipedia .org /wiki /France for "France" in EnWiki. (For interpretation of the references to color in this table, the reader is referred to the web version of this article.)

	Country	EnWiki		ArWiki		RuWiki
		K	K *	K	K *	K	K *
	United States (US) OC	1	9	1	5		2 7
	France (FR) RC	2	1 9	3	3 1		1 4
	United Kingdom (UK) OC	3	2 5	6	2 0		3
	Germany (DE) RC	4	3 3	8	1 4		2 4
	Canada (CA) OC	5	2 6	1 3	1 9	1	2 6
	India (IN) PIC	6	23	9	25		8
	Australia (AU) OC	7	3 5	1 6	2 2	1	1 2
	Italy (IT) RC	8	1 5	5	1		3 2
	Japan (JP) PUC	9	4	1 1	9	1	7
	China (CN) PUC	1 0	8	1 2	1 7		2 1
	Russia (RU) BC	1 1	6	7	2		2
	Spain (ES) RC	12	30	4	8		15
	Poland (PL) RC	13	12	26	32		17
	The Netherlands (NL) RC	14	37	18	33		31
	Iran (IR) YC	1 5	2	1 4	1 5	3	2 2
	Brazil (BR) GC	1 6	3	2 1	2 6	2	1
	Sweden (SE) RC	17	22	22	7		5
	New Zealand (NZ) OC	18	28	34	24		4
	Mexico (MX) GC	19	40	23	38		37
	Switzerland (CH) RC	20	38	20	34		18
	Norway (NO) RC	21	32	35	16		11
	Romania (RO) RC	22	10	19	6		36
	Turkey (TR) YC	2 3	7	1 5	1 3	2	3 8
	South Africa (ZA) OC	24	24	29	39		20
	Belgium (BE) RC	25	18	27	37		30
	Austria (AT) RC	26	39	28	28		28
	Greece (GR) RC	27	21	10	36		25
	Argentina (AR) GC	2 8	1	3 2	2 9	3	2 3
	Philippines (PH) PIC	29	17	36	21		33
	Portugal (PT) RC	30	36	24	12		9
	Pakistan (PK) PUC	3 1	5	2 5	3 5	3	2 9
	Denmark (DK) RC	32	16	33	10		19
	Israel (IL) YC	33	20	17	18		6
	Finland (FI) RC	34	14	37	4		16
	Egypt (EG) YC	35	31	2	3		39
	Indonesia (ID) PIC	36	13	31	11		10
	Hungary (HU) RC	37	11	40	40		40
	Taiwan

(TW) PUC 38 27 39 27 34 South Korea (KR) PUC 39 34 38 30 35 Ukraine (UA) BC 40

	29	30	23	13

Table 2

 2 Cross-edition direct friends and followers extracted from G R matrix (top table) and from G qrnd (bottom table) for the top countries of each area. For each top country, we list the direct friends (followers) present in the direct friends list given by all five Wikipedia editions, the ones present in 4 editions out of 5 and the ones present in 3 editions out of five.

	Top country	G R Wiki friends present in		G R Wiki followers present in
		all 5 editions	4 out of 5 editions	3 out of 5 editions	all 5 editions	4 out of 5 editions	3 out of 5 editions
	US	FR	DE	UK	MX-CA	IL	UK
	BR	US-FR	DE		AR-PT		MX
	FR	US	DE		BE	ES	IT
	RU	US-FR	DE		UA-FI		PL
	TR	US-FR	DE		GR-IR
	JP	US-FR	DE		KR-TW-CN	PH
	IN	US-FR		DE	PK-ID		ZA
	Top country	G qr Wiki friends present in		G qr Wiki followers present in
		all 5 editions	4 out of 5 editions	3 out of 5 editions	all 5 editions	4 out of 5 editions	3 out of 5 editions
	US	CA	UK-MX	FR		UK	CA-MX
	BR	PT-AR	ES-MX		AR	PT	UK
	FR	IT-DE		US-BE		UK-BE-ES	CH
	RU	UA	DE	CN-PL-US	FI	UA-PL	IR
	TR	GR	IR-RU		GR-IR	EG-RO
	JP		CN-TW-US-KR		KR-CN-TW
	IN	PK-CN	ID	IR	PK-ID		CN

Acknowledgements

This work was supported by APR 2015 call of University of Toulouse and by Région Occitanie (project GOMOBILE), CNRS MASTODONS-2016 project APLIGOOGLE, and EU CHIST-ERA MACACO project ANR-13-CHR2-0002-06.


Sylvain Rodat

Stéphane Abanades

Gilles Flamant

Hydrogen production from natural gas thermal cracking: design and test of a pilot-scale solar chemical reactor

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

Results show the strong influence of temperature and residence time on the chemical conversion, C 2 H 2 is the main byproduct. Significant quantities of carbon black were recovered and analysed: the higher the temperature, the higher the specific surface area.

After the operation of a 10 kW solar reactor, a 50 kW reactor was designed, built and tested at the 1 MW solar furnace of the laboratory. The indirect heating reactor is composed of a graphite cavity (approaching the black-body behaviour) crossed by seven single graphite tubes (80 cm length). The cavity is separated from the ambient oxidizing atmosphere by a domed quartz window. A filter bag permits to separate carbon particles from the gaseous products. For 900 g/h of CH 4 injected (50% molar, the rest being argon) at 1800K, this reactor produced 200 g/h H 2 (88% H 2 yield), 330 g/h CB (49% C yield) and 340 g/h C 2 H 2 with a thermal efficiency of 15%. A 2D thermal model of the reactor was developed. It showed that the design of the reactor front face could be drastically improved to lower thermal losses. The optimized design could reach 77% of the ideal black-body absorption efficiency (86% at 1800K), i.e. 66%. A preliminar economic analysis at 55 MW scale shows that this process can be competitive with the conventionnal process of hydrogen production that is to say, the steam methane reforming.

  Projected total cost: 3.2 m€ Maximum EC contribution: 1.9 m€ Co-ordinator's e-mail address: Flamant@promes.cnrs.fr Project web site -URL address: http://www.promes.cnrs.fr/ACTIONS/Europeenes/solhycarb.htm Duration: March 2006-February 2010 (4 years) Hydrogen production from natural gas thermal cracking: design and test of a pilot-scale solar chemical reactor Project funded by the European Commission, FP6, Contract SES-CT2006-19770 Sylvain Rodat, Stéphane Abanades, Gilles Flamant PROMES-CNRS, France Solar methane decarbonization aims at dissociating methane into two valuable products: hydrogen and carbon black.

  Figure 2: CH 4 conversion, H 2 yield, and C yield versus temperature for the first experimental series (Ar: 31.5 NL/min, CH 4 : 10.5 NL/min)

Figure 3 :

 3 Figure 3: Carbon black specific surface area versus temperature

Figure 5 :Figure

 5 Figure 5: Economic analysis (Hydrogen production price vs carbon black selling price)