Γεωπονiκο Πανεπiστημiο

Τροφiμων Τεχνολογiασ

Εργαστηρiο

Prof E George-John

Nychas

Evanthia Manthou

Gwendoline Coeuret

Stephane Chaillou
email: stephane.chaillou@inrae.fr

George-John E Nychas

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ HELLENIC REPUBLIC

Keywords: Ready-to-eat pineapple, spoilage, fungal diversity, metagenetic analysis, temperature 31

The initial pineapple composition largely determined the spoilage progress  The temperature and storage time constitute the second most influencing factors of pineapple spoilage  The impact of temperature and storage time varied according to the initial prevalent fungal species

influencing spoilage and their impact was depending on the initial prevalent fungal species, which 25 showed different responses to the various modifications. Our results strongly suggest that further

Introduction 34

Fresh-cut market has grown dramatically in recent years, as a result of changes on consumers' 35 attitude. Ready-to-eat (RTE) fruits and vegetables fulfil the growing demand for healthy, convenient 36 and minimally processed food products [START_REF] Gorni | Microbiome profiling in fresh-cut products. 441[END_REF]Qadri et al., 2015). However, the quality 37 and safety assurance of these new types of fresh products is a major challenge for the fresh-cut Fresh-cut fruits and vegetables products have a limited shelf life due to accelerated physiological and 41 biochemical changes occurring during their processing and storage (Zhang et al., 2014;Torri et al., 42 2010;Di Egidio et al., 2009). Indeed, the processing treatments render the products more prone to 43 spoilage microorganisms, as well as micro-organisms of public health significance (Qadri et al.,44 2015; [START_REF] Leff | Bacterial Communities Associated with the Surfaces of Fresh Fruits and 461 Vegetables[END_REF]. Various studies underline the presence of phytopathogens and human 45 pathogens, but also microorganisms with antagonistic properties against these pathogens, which have a significant influence on human health and products' quality [START_REF] Gorni | Microbiome profiling in fresh-cut products. 441[END_REF]. Therefore, a better 47 insight into the microbial community and its potential interactions in food associated matrices is 48 required to provide safe and high-quality food (Cao et al., 2017;[START_REF] Juste | Recent advances in molecular techniques to study 455 microbial communities in food-associated matrices and processes[END_REF]. pineapple. To our knowledge, metagenetic analysis has never been applied to the pineapple 75 microbiota. Therefore, this work sheds light on the variability of RTE pineapple's spoilage 76 microbiota and on how it is changing during shelf life with the influence of the temperature used 77 during storage.

DNA extraction of the plate microbiota 110

After the enumeration of the microbial populations, appropriate countable RBC plates were selected.

111

All the colonies present on the surface of each plate were suspended in 2 ml Ringer buffer solution 112 (Lab M Limited), harvested with a sterile pipette and transferred in a 2 ml vial. The microbial vials 113 were stored by freezing at -80 o C supplemented with 50% (v/v) sterile glycerol.

114

Microbial DNA was extracted as previously described by [START_REF] Hoffman | A ten-minute DNA preparation from yeast efficiently releases 443 autonomous plasmids for transformation of Escherichia coli[END_REF] with slight 115 modifications. Briefly, 0.3 ml of lysis solution and 0.3 ml of phenol/chloroform were added in the 116 microbial pellets obtained after centrifugation (for the removal of glycerol). The solution was 117 transferred in tubes with 0.3g of glass beads which were then placed in vortex for 4 minutes. The 118 tubes were centrifuged for 2 minutes at 13,000 rpm and the supernatant carefully transferred at 1.5ml 119 tubes. 800 μl of 100% ethanol were added and the tubes were centrifuged at the same conditions. 120 After the centrifugation, 1ml of 70% ethanol was added, the tube was centrifuged again and the 121 supernatant was discarded. The DNA was resuspended in100 μl of TE buffer solution and stored

Results

171

Growth of dominant fungal microbiota is temperature dependent

A comparative analysis of total viable mesophilic counts (TVC) and fungal microbial counts on four 173 independent pineapple batches revealed that fungi and mostly yeasts are the main component of the 174 cultivable microbiota over storage (Figure 1). Bacterial population, for both Pseudomonadaceae and 175 Enterobacteriaceae families commonly found on vegetables and fruits, was therefore very low with 176 no more than 2 log CFU/g throughout storage at all the studied temperatures (data not shown).

177

Moreover, the population of lactic acid bacteria was not detectable with common microbiological 178 analyses due to the dominance of yeasts on MRS agar plates. As it could be expected, the growth of 179 the fungal population was faster at the highest temperatures. The initial level of fungi (mean ± As far as the pH is concerned, no significant differences on pH measurements were found between 189 the different temperatures and during storage (Table 1).

Fungal OTU richness and alpha-diversity is different between pineapple samples and

The effect of temperature and time of storage on fungal diversity.

207

The effect of different temperatures and storage times was analysed on fungal richness after merging

208

OTUs at species-level (Figure 3). The species' richness was significantly higher in pineapple

Discussion

273

The aim of the present study was to characterize the microbial community involved in the spoilage of 274 RTE pineapple and determine the changes of the diversity when stored under different temperatures, 275 using a metagenetic approach.

276

Our results demonstrated that fungi and mainly yeasts were the predominant spoilage 277 microorganisms found in RTE pineapple. Not surprisingly, the high yeast population is likely 278 attributed to the high level of sugars and the low pH of pineapple, which is ideal for their growth 279 [START_REF] Leneveu-Jenvrin | Changes of 463 Quality of Minimally-Processed Pineapple (Ananas comosus , var . 'Queen Victoria') during Cold 464 Storage : Fungi in the Leading Role[END_REF]Da Cruz Almeida et al., 2018;[START_REF] Maciel | The diversity and antifungal susceptibility of the yeasts isolated from coconut 472 water and reconstituted fruit juices in Brazil[END_REF]. Previous works, 280 recorded similar levels of mesophilic populations and fungi in pineapple (Leneveu-Jevrin et al., 281 2020;Di Egidio et al., 2009;Montero-Calderon et al., 2008;[START_REF] Tournas | Moulds and yeasts in fruit salads and fruit juices[END_REF]. Two of these 282 studies also pointed out significant differences on the initial and final microbial values depending on 283 the different batches (Leneveu-Jevrin et al., 2020;[START_REF] Tournas | Moulds and yeasts in fruit salads and fruit juices[END_REF].

Although cultural methods have been extensively be used in food microbiology, they are also 285 considered extremely biased in their ability to capture the microbial diversity of complex 286 environments (Cao et al., 2017;Edet et al., 2017;Ercolini et al., 2013). Consequently, we firstly 287 proceeded to a comparative analysis of the culture-dependent and culture-independent 288 characterization of fungal community of pineapple. We were able to demonstrate that a whole 289 phylum (Basidiomycota) was hardly detected in plates, while one of the most abundant species 290 detected in one batch (Fusarium circinatum) was unsuccessfully represented in plates' microbiota.

291

To our opinion, this important finding indicates that non-cultural analytical methods should be 292 advised for further microbiota analysis of pineapple.

293

The effect of temperature and storage time on fungal diversity of pineapple samples was further region, and agricultural practices [START_REF] Leff | Bacterial Communities Associated with the Surfaces of Fresh Fruits and 461 Vegetables[END_REF].

303

In the present work, the two batches (P3 and P4) had similar composition, since the phylogenetically in composition between the various studies. As it was mentioned above, these differences could be 325 attributed to various pre-and pro-harvest environmental factors, agricultural practices, but also plant 326 genotype. Additionally, there is a low species diversity in previous studies which may be related to 327 the biases of culture-dependent techniques (as we discussed above) or the limitations of conventional 328 genomic methods [START_REF] Subasinghe | Evaluation of 511 denaturing gradient gel electrophoresis ( DGGE ) and next generation sequencing ( NGS ) in 512 combination with enrichment culture techniques to identify bacteria in commercial microbial-based 513 products[END_REF].

329

In the light of this scientific literature and by comparing them with the data obtained in our work, it 330 is plain that pineapple may harbour a vast variety of fungal microbiota. However, our study provide circinatum. Multiple species of Fusarium are associated with fruit rot and leaf spot diseases of fruits 335 and especially pineapple [START_REF] Jacobs | Fusarium ananatum sp . nov . in the Gibberella fujikuroi species complex from 452 pineapples with fruit rot in South Africa[END_REF]. However, at the later stages of spoilage in batch P1,

38

  industry and requires full involvement and increasing investigations of food scientists (Mederos et 39 al., 2020).

  40

  fresh-cut pineapple were supplied by a local manufacturer in Athens. The pineapple 82 was packed in PVC trays each of one containing 220 g of fruit. The trays were transported to the 83 laboratory within 24 hours from their production and stored at three different isothermal 84 temperatures, 4, 8, 12 o C and under dynamic temperature conditions (8 h at 4 o C, 8 h at 8°C and 8 h at 85 12 o C) in high precision (±0.5) incubators (MIR-153, Sanyo Electric Co., Osaka, Japan). The 86 incubation temperature was recorded every 15 minutes using electronic temperature devices (COX 87 TRACER®, Cox Technologies Inc., Belmont, NC, USA). The first sampling was conducted at the 88 time of pineapple arrival to the laboratory and also at 38 h, 72 h, 134 h and 230 h of storage for 4, 89 8 o C and the dynamic conditions. The final sampling point for 12 o C was 134 h. 25 g of pineapple) were aseptically transferred into a sterile Stomacher bag, (Seward 93 Medical, London, UK), diluted with 225 ml of Ringer buffer solution (Lab M Limited, Lanchashire, 94 UK) and homogenized for 60 s at 230 rpm in a stomacher device (Lab Blender 400, Seward Medical, 95 London, UK). The appropriate decimal progressive dilutions were prepared and the following 96 microbial determinations were performed: total mesophilic microbial populations (total viable 97 counts, TVC) by the spread method on tryptic glycose yeast agar (Plate Count Agar, Biolife, Milan, 98 Italy) , after incubation of plates at 25 o C for 72 h; yeast and moulds by the spread method on rose bengal chloramphenicol agar (RBC, Lab M Limited) and incubation at 25 o C for 3-5 days; 100 Pseudomonas spp. by spread method on pseudomonas agar base with selective supplement 101 cephalothin-fucidin-cetrimide (CFC, Lab M Limited) at 25 o C for 48 h; lactic acid bacteria by pour 102 method on de Man, Rogosa and Sharpe agar (MRS, Biolife) at 30 o C for 72 h; and bacteria of the 103 Enterobacteriaceae family by pour method on violet red bile glucose agar (VRBG, Biolife) and 104 incubation at 37 o C for 24 h. The results were expressed as the average (± standard deviation, n=4) 105 log colony forming units per gram (log CFU/g) of fruit. 106 The pH values of fruit samples were measured with a digital pH meter (RL150, Russell pH Cork, 107 Ireland) with a glass electrode (Metrohm AG, Herisau, Switzerland).108 109

122

  overnight at 4 o C. Before further analysis, 1 μl of RNase was added and DNA incubated for 15 123 minutes at 37 o C.

  each pineapple sample were homogenized with 20 ml Ringer buffer solution (Lab M 127 Limited) in filter Stomacher bag (Interscience, St-Nom, France) for 60 s in the stomacher device. 128 Then, 20 ml of the juice were collected in 50 ml tubes (SARSTEDT AG & Co. KG, Germany) and 129 centrifuged (Heraeus Multifuge 1S-R, Thermo Electron Co.) at 8000 × g for 20 min at 4 o C. Since the 130 supernatant was discarded, the microbial pellet was washed with 20ml of distilled-dionized water 131 and centrifuged (Heraeus Fresco 21, Thermo Scientific) again at the same conditions. The cells were 132 rediluted in 1.7ml sterile ultrapure water, transferred in 2 ml eppendorfs (SARSTEDT AG & Co. 133 KG), and centrifuged at 17000 x g for 10 minutes at 4 o C. The supernatant was discarded and the 134 microbial cells were stored at -80 o C. Microbial DNA was extracted according to the protocol 135 described above for plates. constructed following two rounds of PCR amplification. The first 139 amplification of the ITS2 rRNA gene was performed with the primers ITS3 (5'-GCATCGATGAAG 140 AACGCAGC-3') and ITS4 (5'-3'TCCTCCGCTTWTTGWTWTGC-3'). The final primer 141 concentration used was 10 μM. Forward and reverse primers carried the Illumina 5'CTTTCCCTAC 142 ACGACGCTCTTCCGATCT-3' and the 5'-GGAGTTCAGACGTGTGCTCTTCCGATCT-3' tails, 143 respectively. The first round of PCRs was performed with the high-fidelity AccuPrime Taq DNA 144 polymerase system (Invitrogen, Carlsbad, USA) and 5 μL of microbial DNA. The cycling conditions 145 were: 94 o C for 1 min, followed by 30 cycles of amplification at 94 o C (60 s), 55 o C (60 s), and 72 o C 146 (60 s), with a final extension step of 10 min at 72 o C. The amplicon size, quality, and quantity of the 147 amplified DNA were checked on a DNA1000 chip (Agilent Technologies, Paris, France). Then, the 148 second Miseq PCR was conducted with V3 illumina MiSeq kit as described in Poirier et al. (2018). Raw read sequences were deposited at the Sequence Read Archive under the Bioproject number 150 PRJNA665125 and the accession numbers SAMN16242305 to SAMN16242366. filtering of reads and taxonomic assignment of Operational Taxonomic Units (OTU) 153 Raw sequencing reads were imported into the FROGS (Find Rapidly OTUs with Galaxy Solution) 154 pipeline (Escudie et al., 2017) for quality control and assembly into OTU. Roughly, the pipeline was 155 as follow: quality-filtered ITS2 paired-end sequences were merged with VSEARCH v2.15.0 (Rognes 156 et al., 2016) using 0.1 mismatch rate in the overlapped region. Only amplicon with a size above 150 157 bp and no longer than 500 bp were kept. Merged amplicon sequences were dereplicated and 158 clustered using SWARM v3.0.0 (Mahe et al., 2015) algorithm with a distance threshold of 3. 159 Chimeras were removed with VSEARCH v2.15.0. The resulting sequences were filtered for spurious 160 OTUs by keeping only those with at least 0,01% of relative abundance within the whole dataset 161 (Auer et al., 2017). Taxonomic assignment of OTUs was performed using the UNITE 6.1 ITS2 as 162 reference database (Nilsson et al., 2018 https://unite.ut.ee/) and the Blastn+ algorithm (Camacho et 163 al., 2009).

  of alpha and beta diversity 166 Fungal diversity was analysed using the R package Phyloseq(McMurdie and Holmes, 2013). OTU 167 abundance was normalized using the median sequencing depth of all samples. Analyses of alpha and 168 beta diversity were carried out using standard or custom Phyloseq command lines. 169 170

209

  samples stored at 4 o C (p<0.01). The samples stored at dynamic conditions and 8 o C followed, while 210 the samples stored at the highest temperature (12 o C) had the lowest number of species. The fungal richness was also comparable for the different storage time (p<0.01). At the beginning of the storage 212 (zero time), the diversity was higher compared to all the other storage times. Although the species 213 richness decreased over time, the species' number at 230 hours did not follow the same declining 214 course. This observation is not unexpected, since the samples at 230 hours come exclusively from 215 storage at 4 o C. The corresponding samples (230h) stored at 8 o C and dynamic conditions were not 216 Non-Metric Multidimensional Scaling (NMDS) on Bray-Curtis distances to 219 statistically compare the fungal diversity within the samples of different temperature and time of 220 storage. In all cases (data not shown), communities recovered from a given temperature or storage 221 time did not clustered together on the factorial plane. On the other hand, there were a discrete 222 clustering among samples of the different batches of pineapple, presented in Figure 4. The fungal 223 diversity of most of the samples from batch P1 and P2 differs with that of batches P3 and P4 fungal diversity between the four batches are presented in Figure 5, where the 227 composition plot of relative abundances is illustrated according to Bray-Curtis hierarchical clustering 228 of pineapple samples. In Figure 6 is also presented a phylogenetic tree of the different fungal species 229 based on the ITS2 sequences.230 231 Pineapple samples from batches P3 and P4 had a quite similar fungal community dominated by two 232 phylogenetically related species Candida argentea, and Candida sake from the candidate family 233 Saccharomycetales_incertae_sedis. Most samples from Batches P4 can be distinguish from those of 234 batch P3 with the presence of Hanseniaspora uvarum, which is also closely related phylogenetically 235 to the aforementioned Candida. Pineapple samples from batches P1 and P2, displayed a set of completely different fungal communities dominated by species from the phylogenetically related 237 Nectriaceae (Fusarium) and Metschnikowiaceae (Clavispora/Candida) families. Candida 238 intermedia and Fusarium circinatum were the most abundant species in samples of batch P2, 239 whereas some samples from batch P1 showed higher level of diversity with Pichia fermentans 240 (Pichiaceae) and Meyerozyma caribbica (Debaryomecytaceae).

  , the effect of storage time and temperature varied across the different fungal species.243Interestingly, the initial composition of pineapple microbiota had a great impact on the evolution of 244 spoilage at different temperatures and storage time. Therefore, situations varied from one batch to 1 (Figure7), we observed that both temperature and storage time drove a strong 248 change on the fungal community structure.

  294analysed. Both factors had a significant impact; specifically, species richness decreased over storage 295 time and when the temperature reached higher levels. However, when we compared the fungal 296 diversity within the samples of different temperature and time of storage based on Bray-Curtis 297 distances, no radical clear clustering could be evidenced according to the studied factors. On the 298 other hand, the analysis revealed a significant batch effect on fungal diversity and composition. 299 Leneveu-Jenvrin et al. (2020) also observed that the pineapple communities clustered mostly 300 according to batches and not storage time. The high biological variability is a common observation in 301 plant origin products due to the strong impact of various factors such as cultivar, geographical 302

Figure 2 . 565 Figure 3 .

 25653 Figure 2. Heatmap showing the comparison between fungal species relative abundances

Figure 5 .

 5 Figure 5. Composition plot showing the relative abundances of the nine main Ascomycota

Figure 6 . 582 Figure 7 .Figure 8 .

 658278 Figure 6. Neighbour-Joining phylogenetic tree of the different species based on the ITS2

Table 1 .

 1 180 standard deviation, n=4) was 4.69 ± 0.65 log CFU/g, and reached a final average level of 7.36 ± 0.44 and 7.41 ± 0.72 log CFU/g at 8 o C and 12 o C, respectively. Storage at 4°C revealed more stringent 182 than the three other temperature conditions on growth kinetics. In this case, the fungal population 183 reached only 6.11 ± 0.99 log CFU/g after 230 hours. The microbial growth monitored during 184 dynamic temperature conditions resembled that recorded at 8 o C. The initial and final pH values of pineapple during storage at different temperatures.

	185
	186
	187

pH Storage temperature Initial value Final values 4 o C

		3.60 ± 0.07
	8 o C	3.56 ± 0.06
	3.32 ± 0.25
	12 o C	3.66 ± 0.06
	Dynamic	3.64 ± 0.11

Table 2 .

 2 Fungal OTU richness (merged at different taxonomic levels) between food pineapple

	193
	194	during storage. We compared the fungal diversity by ITS2 amplicon sequencing between DNA
	195	extracted directly from pineapple samples or from the fungal population that grew on agar plates. As
	196	shown in Table 2, the fungal OTU richness was significantly lower on plates.
	197
	199
			Number of genera	Number of species	Number of OTU
		Pineapple samples	22	33	47
		Plate samples	18	25	39

191 cultivation media. 192 We investigated whether cultivation methods were underestimating the level of fungal population 198 samples and agar plate samples. 200 Figure 2 shows how the 33 fungal species detected by non-cultural metagenetic analysis could be 201 detected and quantified from the microbiota recovered from agar plates. In general, detection of most 202 species from Basidiomycota phylum was unsuccessful in comparison to species from Ascomycota 203 phylum. In addition, detection of Fusarium species was also strongly biased on plates, in particular 204 Fusarium circinatum was highly abundant in pineapple samples compared to plates. Therefore, to 205 avoid any bias in our analysis, only data from pineapple samples were used further.

206

  Concerning batch P2 (Figure8), a trend similar to that observed in batch P1 can be drawn 261 with, at time zero, a large dominance of F. circinatum which was progressively replaced by C.

	262
	263	intermedia at high storage temperatures and by C. argentea at 4°C. As shown in both Figure 4 and
	264	Figure 5, the fungal communities from samples of batches P3 and P4 were not affected significantly
	265	by temperature and storage time. Unlike pineapple samples from batches P1 and P2, the fungal
	266	community of batch P3 was covered by the great dominance of C. argentea throughout the storage at
	267	all temperatures (data not shown). C. sake was not affected by temperature or time in P3 but also in
		P4. However, in the case of samples from batch P4, we noticed a slight impact of temperature and
	255
	256	temperature.
	257
		Specifically, C. intermedia succeeded to dominate to samples of 12 °C and 8 °C from the early stages

Temperature was the most influent parameter separating 249 samples stored at 4°C from those stored at 12°C, with in both cases, a gradual change over longer 250 storage time. Samples stored at intermediate temperature of 8°C, clustered at intermediate positions 251 between samples stored at 4°C or 12°C. Only samples stored with a dynamic sequence of 252 temperature scattered randomly with no logical order. Among the most striking changes, we 253 observed that F. circinatum had high abundance (>75%) at zero time of storage, while following the 254 next stages of storage C. intermedia or P. fermentans finally dominated according to the 258 of storage, while P. fermentans in samples of 4 °C at the final stages (134 and 230 h). On the other 259 hand, M. carribica was able to dominate only at the middle of storage (72 h) for 8 °C and dynamic conditions. 268 storage time on H. uvarum and C. argentea. The former became more prevalent at 8 and 12°C in the 269 middle of storage, while the latter prevailed at 4°C throughout storage and at 12°C and dynamic 270 conditions at the early stages of storage.

271 272

  pineapple, mainly based on culture-dependent techniques.[START_REF] Tournas | Moulds and yeasts in fruit salads and fruit juices[END_REF] detected Schwanniomyces polymorphus (formerly known Debaryomyces polymorphus), Candida 311 pulcherrima, Pichia spp. and in low abundances Penicillium spp., while Di Cagno et al. (2010) found 312 Meyerozyma guilliermondii (formerly known as Pichia. guilliermondii) as the only species grown on 313 plates. Chanprasartsuk et al. (2010) identified M. guilliermondii and H. uvarum as the main yeasts of 314 fresh pineapple juices from different locations and countries. These two species were characterized 315 both by culture-dependent and independent techniques (using DGGE). Zhang et al. (2014) used 316 Candida argentea, Candida sake and Meyerozyma caribbica isolates for the investigation of the 317 headspace oxygen level in shelf life of pineapple, since they were previously isolated from spoiled

	305
	306	other hand, most samples from P1 and P2 were dominated by the species F. circinatum or C.
		intermedia which are also phylogenetically related to each other. Moreover, some samples of P1

304

related C. argentea and H. uvarum (only in batch P4) or C. sake were the dominant species. On the 307 showed higher level of diversity, since P. fermentans and M. caribbica were present in some samples 308 in high abundances. There are few previous studies (not NGS studies) concerning the fungal composition of 318 commercial fresh-cut pineapple. Ibrahim et al. (2017) identified Fusarium proliferatum, Fusarium 319 verticillioides, Fusarium sacchari and Fusarium sp. in diseased pineapple tissues. Some of the 320 Fusarium sp. isolates appeared to be phylogenetically related to F. circinatum. Recently, Lima et al. 321 (2019) found that in tropical fruit based ice-creams (including pineapple based) the predominant 322 species were Candida intermedia, Torulaspora delbrueckii, Candida parapsilosis, Clavispora 323 lusitaniae, Saccharomyces cerevisiae and Pichia kudriavzevii. It is obvious that there are differences 324

336

  Pichia fermentans prevailed at 4 o C, while C. intermedia prevailed at 8 and 12 o C. Both P. fermentans 337 and C. intermedia have been studied with great potential in the control of phytopathogenic molds.Colletotrichum sublineolum and Colletotrichum graminicola.Giobbe et al. (2007) investigated the 340 dual nature of a strain of P. fermentans which controls brown rot on apple fruit, but becomes a 341 destructive pathogen when applied to peach fruit. Consequently, it could be postulated that these two 342 yeasts could possibly play a competitive role in supressing the growth of F. circinatum and 343 according to the temperature, one of the two closely related yeasts is able to dominate. The same 344 trend was followed in batch P2, but C. argentea prevailed finally at 4 o C. On the contrary, when C. It is obvious that fresh pineapple products are a very complex and unpredictable ecological niche where the specific spoilage species may have 360 a totally different response to the changes of important environmental factors used for storage and 361 which are important to assess the shelf-life of these RTE fruit. Consequently, further and thorough 362 research are necessary in order to unravel how the various environmental factors of pineapple Di Cagno, R., Cardinali, G., Minervini, G., Antonielli, L., Giuseppe-Rizzello, C., Ricciuti, P., 409 Gobbetti, M., 2010. Taxonomic structure of the yeasts and lactic acid bacteria microbiota of 410 pineapple (Ananas comosus L. Merr.) and use of autochthonous starters for minimally processing.

	551
	552
	411 553
	554
	338	Food Microbiol. 27, 381-389. https://doi.org/10.1016/j.fm.2009.11.012 Figure 1. A)
	339	Rosa-Magri et al. (2011) identified C. intermedia as one of the yeasts with biocontrol activity against
	345
	346	argentea was present in great dominance (batch P3) at first place there was no significant impact of
	347	temperature and time. The conclusion is differentiated (batch P4) when H. uvarum was initially
	348	present together with C. argentea as the second most dominant species. The two closely related
	349	species seem to be affected by the temperature and time in an opposite way, but in a lesser extent.
	350	Consequently, the progress of spoilage firstly depends on the initial composition and secondly is
	351	determined by the effect of temperature and time.
	352
	353	5. Conclusions
	354	The current study significantly contributes to the understanding of the fungal community associated
	355	to fresh-cut and RTE pineapple. It is the first time that the impact of temperature and storage time on
	356	fungal diversity is being studied for a fresh tropical fruit product. The results demonstrated that the
		different batches of pineapple show great variability on fungal composition. The initial composition

357

constitute an important factor on spoilage progress. Depending on the initial prevalent fungal 358 species, the impact of temperature and storage time varies.

TVC populations (mean ± standard deviation, n=4) and B) Fungal populations 555 (mean ± standard deviation, n=4) in RTE pineapple during storage at 4 o C, 8 o C, 12 o C, and 556 dynamic temperature conditions.

  The blue, green, red and orange lines represent the growth of the 557 microbial populations at 4 o C, 8 o C, 12 o C, and dynamic temperature conditions.

Microbiol. 81, 1530-1539. https://doi.org/10.1128/AEM.03470-14

grant from funding agencies in the public, commercial, or 372 not-for-profit sectors.

additional information on how these different microbiotas may behave towards storage conditions. A 332 thorough observation at batch-level reveals various conclusions about the impact of temperature and 333 storage time. Specifically, the batches P1 and P2 were characterized by the great dominance of F.

Di Egidio, V., Sinelli, N., Limbo, S., Torri, L., Franzetti, L., Casiraghi, E., 2009 Alvarez-Ordonez, A., Bolton, D., Bover-Cid, S., Chemaly, M., Davies, R., De Cesare, A., Herman, 424 L., Hilbert, F., Lindqvist, R., Nauta, M., Peixe, L., Ru, G., Simmons, M., Skandamis, P., Suffredini, 425 E., Jordan, K., Sampers, I., Wagner, M., Da Silva Felicio, M.T., Georgiadis, M., Messens, W.,

Declaration of interests

☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Authors declare no conflict of interest

Conflict of Interest


Greqam

Mohamed Belhaj
email: mbelhaj@ec-marseille.fr.

Frédéric Deroïan

Frédéric Deroian
email: eric.deroian@univmed.fr.

Endogenous efforts on communication networks under strategic complementarity

Keywords: JEL Classification Numbers: D85, C72 Communication Network, Endogenous Efforts, Strategic Complements

This article explores individual incentives to produce information on communication networks. In our setting, efforts are strategic complements along communication paths with convex decay. We analyze Nash equilibria on a set of networks which are unambiguous in terms of centrality. We first characterize both dominant and dominated equilibria. Second, we examine the issue of social coordination in order to reduce the social dilemma.

Introduction

On communication networks, agents obtain both direct and indirect informational spillovers. Typically, agents may benefit from the information of their neighbors, the neighbors of their neighbors, and so on. The related theoretical literature is mainly concerned with the strategic formation of links. In this paper, we study the individual incentives to produce information, when agents produce efforts which are strategic complements1 along communication paths. Let us present two series of relevant examples.

The first one concerns protective measures, like computer network security, airline baggage screening, fire safety in apartment buildings, infectious disease vaccination, protection against bankruptcy and theft (see [START_REF] Heal | Interdependent security[END_REF] and [START_REF] Kearns | Economics, computer science, and policy[END_REF]). To give a flavour, consider the resources devoted by air carriers to luggage screening for explosives; the network structure arises from baggage transfers between air carriers. Because risks are correlated, more protective measures set by my neighbor may improve the return of own increased protection. Further, the level of protection of my neighbor's neighbor has an incidence upon my own security level through the combination of her protection levels and that of my neighbor (the probability that a bomb passes from my neighbor's neighbor to me without being detected is a decreasing function of the protection level of her and of my neighbor).

A second class of applications concerns knowledge production, the cost of which may be lowered by social coordination. In the context of joint investments in research, some empirical literature is consistent with the existence of synergies along communication paths. [START_REF] Breschi | Mobility of inventors and the geography of knowledge spillovers[END_REF] and [START_REF] Singh | Collaborative networks as determinants of knowledge diffusion patterns[END_REF] suggest that knowledge spillovers may transit through the social network of inventors (insisting that the probability of knowledge flow decreases with social distance); [START_REF] Hanaki | Dynamics of R&D Collaborations in IT industry[END_REF] recently show that the probability of alliance formation between firms in IT industry is increasing in the number of alliances situated at short distance from the partners (typically until distance 4). Education at school is another case. For example, [START_REF] Hoxby | Peer Effects in the Classroom: Learning from Gender and Race Variation[END_REF] finds evidence of synergies in the performance of students in a classroom, and [START_REF] Calvo-Armengol | Peer effects and social networks in education[END_REF] present evidence of networked effects.

The existence of strategic complementarities in efforts naturally exhibits a social dilemma, in the sense that there exists Pareto-ranked equilibria, and particularly a Paretodominant equilibrium. Given that externalities are networked, we analyze the impact of the position of players on the issue of social dilemma. In particular, we ask the following questions: firstly, does there exist a simple characterization of the Paretodominant equilibrium in terms of players' positions on the network? Secondly, starting from a Pareto-dominated equilibrium, can we provide some appropriate procedure that would take account of the network topology, and which would lead to an equilibrium reducing the social dilemma? Our general answer is that players' centrality may help solving both questions.

To address these issues, we set up a model in which agents produce costly synergic efforts on a fixed communication network. The originality of our approach is that synergies exist between efforts of both directly and indirectly connected agents. More precisely, players aggregate the choice of others through an aggregator (which we name 'inflow of spillovers') which satisfies simple decay assumptions, and payoffs are strategic complements in the players' own actions and the aggregation of the other players' actions. The inflow of spillover is a function of the efforts of other agents along communication paths. We capture the communication aspect by assuming convex decay along communication paths. Our restrictions are mild; in particular, they encompass standard geometric decay (with possible upper bound on communication path length). Some well-know results can be derived from our model. Notably, a dominant equilibrium exists (at the dominant equilibrium, every agent produces more effort than what she produces at any other equilibrium), and it Pareto-dominates all other equilibria.

For the sake of clarity, we begin our analysis with the line network 2 . We first detect an equilibrium such that the ranking of efforts is not aligned with agents' centrality. Can the dominant equilibrium be such? A first proposition states that under very general conditions on utility functions, both dominant and dominated equilibria satisfy that more central agents produce larger effort levels (property P thereafter). This result, which may sound as rather intuitive at first glance, is technically hard to show. First, fixing one equilibrium which both is symmetric (i.e., agents with same structural position have same effort level) and does not satisfy property P , we build the smallestresp. greatest -configuration among those that both dominate -resp. are dominated by -the equilibrium and satisfy property P ; we name this latter configuration the cover -resp. covered -configuration of the former one. The first lemma establishes that if we initiate a simultaneous best-response algorithm (SBRA thereafter) from that cover -resp. covered -configuration, all individual efforts increase -resp. decrease -at each step of the algorithm. In short, the lemma presents a simple procedure, which uses the centrality of agents, and which enables to escape from an equilibrium that does not satisfy property P . A second lemma addresses the characterization of equilibria reached through a SBRA. It shows that a SBRA starting from a symmetric configuration converges to some equilibrium satisfying property P if the equilibrium dominates the cover configuration of the initial one. Finally, a proposition states that, when the initial configuration is the cover (resp. covered) configuration of a symmetric equilibrium, the 'if' part of the second lemma holds. The first proposition follows.

The first proposition characterizes the most socially desirable and undesirable equilibria in terms of the centralities of the agents. One immediate consequence is that, if one detects some equilibrium such that the respective rankings of efforts and centralities are not aligned, then for sure a social dilemma exists, although we are not in the worst case. The second proposition provides another message: if a social dilemma exists, and specifically if the equilibrium is both symmetric and does not satisfy property P , then some initial coordinated impulse to certain agents' efforts, and a dynamic procedure of myopic revisions, is sufficient to reach a configuration which is beneficial to all; furthermore this latter configuration satisfies property P so there is no chance to improve upon by replicating the procedure; last, the initial coordination of impulses is a task which is not demanding for the agents: it can be done by asking agents to adjust once their level of effort to that of one of their neighbor.

Keeping up the degree of generality of utility functions, we extend our results to a class of networks the individual centralities of which are unambiguous. We name it hierarchical communities. Roughly speaking, this architecture is a mixture of trees and symmetric networks, in such a way that neighbors have themselves a close number of neighbors3 . The proofs exhibit no specific difficulty, except that we have to tackle with the following point: inflows are now a function of the values of all paths between agents (typically, one can think about functions like max, min, sum, average, • • • ).

Then, selecting either max or sum functions, we generalize the proofs established on the line network to hierarchical communities networks.

Related literature: This model is related to coordination failures inherent to synergies and spillovers [START_REF] Cooper | Coordinating coordination failures in keynesian models[END_REF]). More specifically, this work inserts in two literatures.

First, our model is related to communication networks (the spillover aspect). In contrast with our article, the literature, issued from the pioneering works of Jackson and Wolinski (1996) and [START_REF] Bala | A noncooperative model of network formation[END_REF], mainly focuses on strategic network formation, and does not assume endogenous efforts. Few models of communication network formation have an explicit treatment of decay4 . With respect to this literature, our paper provides results under very mild restrictions on spillovers, that is we only need to assume that decay is convex.

Second, a literature addresses the issue of good production on networks (the endogenous efforts aspect). In [START_REF] Bramoullé | Public goods in networks[END_REF] and [START_REF] Ballester | Who'swho in networks. Wanted: the key player[END_REF], agents produce a costly effort and benefit from the effort of their neighbors. From these works, our model extends spillovers' channels to a communication network setting. Our model also encompasses the formulation of utility functions described in [START_REF] Ballester | Who'swho in networks. Wanted: the key player[END_REF] in the case all efforts are strategic complements. One major interest of their paper is to show that, if the level of interdependencies is sufficiently low, there is a unique equilibrium in which efforts are proportional to a Bonacich-centrality measure; this measure, as well as uniqueness, is clearly tied to the choice of the utility function. In contrast, we provide results for a wide range of utility functions, and we allow multiple equilibria and related coordination failure issues. This generalization precipitates the restriction of our results to architectures which are unambiguous in terms of centrality measures.

Finally, we mention that some papers address the issue of both network formation and endogenous effort, like [START_REF] Cho | Endogenous formation of networks for local public goods[END_REF], [START_REF] Goyal | R&D networks[END_REF], [START_REF] Goyal | Network formation and social coordination[END_REF], [START_REF] Cabrales | Effort and synergies in network formation[END_REF], and [START_REF] Galeotti | The law of the few[END_REF]. This last article incorporates indirect spillovers with possible decay (in a context where efforts are strategic substitutes).

The article is organized as follows. The next section presents the model, section 3 is devoted to the characterization of equilibria on the line network, while section 4 extends the results to more general networks. Section 5 concludes. All proofs are included in the appendix.

The model

Let N = {1, ..., n} be a finite set of agents, with n ≥ 3. The effort of agent i is denoted δ i . The definition set ∆ is a compact in R and it is common to all agents.

We denote by δ l (resp. δ h ) the lower (resp. upper) bound of ∆. The effort level may represent the amount of time researchers spend inventing a new product. Throughout the article, superscripts refer to effort levels, subscripts to agents. A strategy profile

δ = (δ 1 , • • • , δ n ) may be denoted (δ i , δ -i ) for convenience. Selecting effort level δ i ∈ ∆,
agent i incurs a fixed cost c(δ i ), with c(.) strictly increasing and c(δ l ) = 0.

Agents are placed on specific networks. Nodes represents agents, edges between nodes represent communication links. For the sake of clarity, we will devote next section to the finite line network (section 4 generalizes results to other architectures which we formally define thereafter). Let index i quote for the position of agent i on the line. Links are undirected. A link between agents i and j is written i : j. The set of links of the line network is {1 : 2, 2 : 3, • • • , n -1 : n}. The path p i,j from agent i to agent j, with j > i (resp. j < i) without loss, is the sequence of distinct nodes

{i + 1, i + 2, • • • , j} (resp. {i -1, i -2, • • • , j}).
We denote by δ(p) the vector of effort levels of the agents placed on path p. A configuration of effort δ is symmetric if any pair of agents with same structural position have same effort level; that is,

δ i = δ n-(i-1) .
Let δ k denote a vector of effort levels with k elements. Denote by R the space of all

possible vectors δ k , for k ∈ {1, 2, • • • , n}.
We define the value of a path p as a function v related to effort levels δ(p) on the path:

R → R + δ → v( δ)
The value v( δ(p i,j )) may be interpreted as the amount of externality that agent i captures from joining agent j through path p i,j . We may abuse the language by evoking the value of a path rather than the value of effort profile associated with a path.

Throughout the paper, we provide function v with three assumptions which grasp the communication aspect of the model. Firstly, we assume that function v is increasing in its arguments. Assumption 1 states this formally:

Assumption 1 For all δ k , δ k in R 2 such that δ k ≤ δ k , we have v( δ k ) ≤ v( δ k ).
Put differently, the value of a path increases if agents on the path produce more effort. Secondly, information travels with possible decay:

Assumption 2 For any sequence of effort levels (δ a , δ b , • • • , δ r ) ∈ R, for every δ q ∈ ∆, v(δ q , δ a , δ b , • • • , δ r ) ≤ v(δ a , δ b , • • • , δ r )
Assumption 2 states that the value of a path decreases if we add a new intermediary at the beginning of the path. Note that the assumption expresses weak inequality.

Notably, this formulation encompasses bounded communication.

Assumption 3 If v(δ a 1 , δ b 1 , • • • , δ r 1 ) ≤ v(δ a 2 , δ b 2 , • • • , δ r 2 ), then for all δ q ∈ ∆, v(δ a 1 , δ b 1 , • • • , δ r 1 ) -v(δ q , δ a 1 , δ b 1 , • • • , δ r 1 ) ≤ v(δ a 2 , δ b 2 , • • • , δ r 2 ) -v(δ q , δ a 2 , δ b 2 , • • • , δ r 2 )
Assumption 3 states that the loss which results from extending the path with some given effort at the beginning, is increasing in the value of the path. In a word, decay increases with the value of the path. This condition is quite general; in particular, it is satisfied in the case of geometric decay. Let I(δ -i ) denote the global externality received by agent i (indifferently labeled the inflow of agent i). For simplicity, we assume an additive formulation of the global externalities that agents capture from the network:

∆ n-1 → R + (δ 1 , • • • , δ i-1 , δ i+1 , • • • , δ n ) → I(δ -i ) = j =i v( δ(p i,j ))
Individual payoffs then are computed as follows:

∆ n → R + δ → Π i (δ i , δ -i ) = π(δ i , I(δ -i )) -c(δ i )
To be consistent with our communication context, we assume that function π(., .) is increasing in both arguments. Furthermore, the profit function satisfies a standard definition of synergic efforts:

Definition Function π is increasing in differences if: for all i ∈ {1, 2, • • • , n} and every pair (a, b) ∈ ∆ 2 with a < b, if I(δ -i ) ≤ I(δ -i ), then π(b, I(δ -i )) -π(a, I(δ -i )) ≤ π(b, I(δ -i )) -π(a, I(δ -i ))
We shall say that efforts are strategic complements along communication paths if function π satisfies the increasing difference property.

This definition expresses that when an agent increases his effort level, the increase of his benefit is strictly larger, the higher the value of the inflow that he receives5 .

Example 1

Geometric decay with possible upper bound B ∈ N on the length of communication paths:

v(δ i 1 , δ i 2 , • • • , δ iq ) = Π min(B,q) k=1 δ i k
The profit function is written:

π(δ i , δ -i ) = δ i × I(δ -i ) -c(δ i )
with δ m ≤ 1. This formulation exhibits strategic complementarity in individual efforts.

Note that the value function satisfies assumptions 1 and 2. As producing effort, agents may for instance access some valuable knowledge, with all pieces of knowledge being complementary: the return of the effort of one agent is increasing in others' amount of knowledge. For instance, researchers may be more productive when the knowledge they receive from the community is increased. If efforts are exogenous (m = 1), we obtain the payoffs of connections' model (net of link formation costs) [START_REF] Jackson | A Strategic model of economic and social networks[END_REF]).

Example 2 Spillovers from direct neighbors [START_REF] Ballester | Who'swho in networks. Wanted: the key player[END_REF]):

v(δ i 1 , δ i 2 , • • • , δ iq ) = δ i 1 if q = 1, 0 otherwise.
The profit function is written:

π(δ i , δ -i ) = δ i - σ 2 δ 2 i + γδ i × I(δ -i )
We analyze Nash equilibria in pure strategies: a strategy profile is Nash if for every agent, her current strategy is a best-response to the current strategies of all other agents. Formally, a profile of individual strategies

δ * = (δ * 1 , • • • , δ * n
) is a Nash equilibrium of the game on the network g if and only if, for every agent i ∈ N , if

δ i = δ * i , π i (δ * i , δ * -i ; g) ≥ π i (δ i , δ * -i ; g).
Note that individual participation constraints are always satisfied in the game since the smallest effort level is costless. A dominant equilibrium, say δ d , is such that for all existing equilibrium δ * , δ * i ≤ δ d i for all i. Symmetrically, a dominated equilibrium, say δ dd , is such that for all existing equilibrium δ * , δ * i ≥ δ dd i for all i.

Finally, we briefly introduce some notations related to the SBRA. Define an infinite sequence of rounds r = 0, 1, 2, • • • Fix some initial configuration δ 0 . Then, at each round r ≥ 1, let all agents revise simultaneously their strategy in response to the configuration δ r-1 , and denote δ r this new configuration. The SBRA may eventually converge to some equilibrium configuration which we denote δ ∞ .

Results on the line

Games with strategic complementarity contain often social dilemmas. Notably, a dominant equilibrium, socially attractive, often exists.

Preliminary

We begin the analysis with recalling a well-known result about existence of Nash equilibria and dominant equilibria in our game.

Preliminary result 1 There always exists a Nash equilibrium in pure strategies. Furthermore, a dominant Nash equilibrium exists, as well as a dominated one. In both, symmetric agents produce the same effort level. The dominant (resp. dominated) equilibrium is easily accessed through a SBRA with initial efforts set at maximal (resp. minimal) level.

(we omit the formal proof, see [START_REF] Topkis | Equilibrium points in nonzero-sum n-person submodular games[END_REF]) To give a flavor, existence is related to the strategic complementarity of the game. Starting from the configuration where all agents exert a maximal effort level, we apply the SBRA. Firstly, this algorithm converges since effort levels are bounded below and we have the increasing differences property: at the end of each iteration, the effort level of every agent does not exceed the one he had at the beginning of the iteration. Secondly, at each step of iteration, symmetric agents produce the same effort level since they simultaneously revise their strategy. Thirdly, the SBRA converges to the dominant equilibrium: at each stage of the algorithm, no agent selects some effort level below the one he exerts at any equilibrium, due to increasing return property; in a word, no agent can 'bore' a configuration which is an equilibrium. This result is more general than our networked context, and only assumption 1, in combination with the increasing difference property, are required.

A counter-intuitive example

Since agents are generally not symmetrically positioned on the line6 , equilibrium configurations of efforts may not be homogenous. One basic observation is that for any homogenous configuration of efforts, more central agents receive more externality. Then, we may expect that equilibria satisfy the following property:

Property P More central agents produce higher effort levels.

We name P -equilibrium an equilibrium satisfying property P . Actually, equilibria, and even the dominant and the dominated one, need not necessarily be P -equilibria.

For instance, consider the case of the dominant equilibrium, which is accessible when running the SBRA with all initial efforts set at the upper bound. At the end of first round, more central agents clearly produce more effort. However, inflows are not necessarily increasing toward the center of the line. The larger the agent's effort, the greater the inflow of her neighbors; therefore property P needs not being satisfied at each stage of the algorithm. And actually, a simple example show that there exist equilibria which do not satisfy property P . This example obtains under geometric decay (which satisfies the three assumptions). Consider n = 8, ∆ = {δ 1 , δ 2 , δ 3 } (hence δ 1 = δ l and δ 3 = δ h ), with δ 1 = 0.02, δ 2 = 0.32, δ 3 = 0.45. Consider the symmetric profile of efforts (δ 2 , δ 3 , δ 2 , δ 1 , δ 1 , δ 2 , δ 3 , δ 2 ). Direct computation indicates that the inflows of agents 1 to 4 are I 1 0.59, I 2 0.65, I 3 0.61, I 4 0.54 (the inflow of other agents is deduced by symmetry). Thus, there is the same ordinal ranking between efforts and inflows.

We conclude that there exists a cost profile under which this configuration is stable;

for instance a Nash equilibrium obtains if c 1 = 0, c 2 = 0.179, c 3 = 0.260.

Main results

Among all equilibria, the dominant equilibrium is socially desirable. Indeed, since individual payoffs are increasing in the inflows, the dominant equilibrium Pareto-dominates all other Nash equilibria. Next proposition makes a link between the position of agents on the line and their level of effort at both dominant and dominated equilibria:

Proposition 1 Both dominant and dominated equilibria are symmetric P -equilibria.

To establish the proposition, we prove two successive lemmata and a second proposition.

Before presenting the lemmata, we define the notions of cover and covered configurations associated with any symmetric configuration. Consider a symmetric configuration δ. The cover configuration δ H is the unique smallest element of the set of configurations which both dominate δ and satisfy property P ; the covered configuration δ L that we set up is the largest element of the set of configurations that both satisfy property P and are dominated by δ. Figure 1 illustrates how we build the required configurations. We will see later on that the cover configuration of an equilibrium is crucial to our analysis.

Technically, we apply the following algorithm: denote by i 0 the index of the central agent:

i 0 = n+1 2 if n is odd, i 0 = n 2 + 1 otherwise. First, we set δ H 1 = δ 1 .
Then, stage 1 proceeds as follows: consider the efforts of agents 1 and 2. If δ 2 ≤ δ 1 , we set δ H 2 = δ 1 , otherwise we set δ H 2 = δ 2 . Stage 2 replicates stage 1 with agents 2 and 3; that is, If δ 3 ≤ δ 2 , we set δ H 3 = δ 2 , otherwise we set δ H 3 = δ 3 . Then we iterate the process until agent i 0 . Since the configuration δ is symmetric, we do the same at the right side of agent i 0 , that is we set δ H n+1-i = δ H i for all i < i 0 (if n is even, we also set δ H i 0 +1 = δ H i 0 ). We proceed similarly with the covered configuration, except that we start from the center to the extremities of the line (decreasing the effort of agents such that their more central neighbor is lower). Note that both the cover and covered configurations are symmetric. Further, this algorithm enables to obtain those configurations after a unique revision of individual strategies.

We are now able to state our first lemma (which contains the main technical difficulties):

Lemma 1 Consider a symmetric equilibrium δ. Then, if a SBRA starts from its cover (resp. covered) configuration, all agents produce a higher (resp. lower) effort level after round 1. Formally, if

δ 0 = δ H (resp. δ 0 = δ L ), then δ 1 ≥ δ 0 (resp. δ 1 ≤ δ 0 ).
(Proof in the appendix) Remark that, by increasing difference property, it is actually true that δ r ≥ δ r-1 (resp. δ r ≤ δ r-1 ) for all r = 1, 2, • • • , ∞. The lemma may not hold if the initial configuration is not an equilibrium, even if it satisfies property P . Again, we would like to insist that, although intuitive at first glance, the result is not trivial.

More precisely, the shape of the cover configuration (like an 'Inca' pyramid) enables the comparison of inflows received by agents with same level of effort, which is critical to obtain our result. In opposite, if we start from a configuration that dominates the equilibrium, we are not sure that it converges to an equilibrium which strictly dominates the initial equilibrium.

Lemma 1 provides sufficient conditions for escaping from some equilibrium; indeed, if the equilibrium that we start from does not satisfy property P , its cover configuration is distinct from it, and for sure we escape from the initial equilibrium. We now turn to the characterization of equilibria toward which a SBRA converges. Next lemma gives some condition under which the SBRA starting from a symmetric configuration (not necessarily an equilibrium) converges to a P -equilibrium.

Lemma 2 Initiating the SBRA from a symmetric configuration, if the converging configuration dominates its cover configuration, then the converging configuration is a Pequilibrium.

(Proof in the appendix) This lemma is rather general, but conjectural. The next proposition provides sufficient conditions for the 'if' part of lemma 2 to be valid:

Proposition 2 Consider a symmetric equilibrium δ that does not satisfy property P .

Starting from its cover (resp. covered) configuration, the SBRA converges to a symmetric P -equilibrium.

(proof omitted) Proposition 2 is a direct application of lemma 1 and lemma 2. Proposition 1 stems immediately from lemma 1 and proposition 2 (proof omitted).

The message behind proposition 1 is that if we detect an equilibrium which does not satisfy property P , then for sure the equilibrium is not dominant. Then, Proposition 2 provides our second main message. In a word, if we detect a symmetric equilibrium δ which does not satisfy property P , providing an appropriate collection of impulses in efforts, and thus letting agents myopically revise their strategies without any central coordination, the procedure reaches an equilibrium which is beneficial to all. This result is interesting from the point of view of the social dilemma. Furthermore, the converging configuration is a P -equilibrium, which means that we cannot do better (since the new equilibrium confounds with its cover configuration). Finally, starting from an equilibrium, accessing its cover configuration is not very demanding. Indeed, following the algorithm of the construction of the cover configuration, it is sufficient to ask agents a unique adjustment of their effort level to their more peripheral neighbor.

Hierarchical communities

In this section, we develop our results established on the line to some other networks.

We only present the extension of lemma 1. The other lemma and the two propositions established in the preceding section follow directly.

Example. We build the following class of trees. There is a sequence of q integers

p 1 , p 2 , • • • , p q with p 1 ≥ p 2 ≥ • • • ≥ p q .
This class of tree is built recursively as follows.

Start with one agent say i 0 , denote by class-1 the set {i 0 }, and build p 1 links involving agent i 0 ; label agent i 0 's neighbors class-2 agents. Then, considering every class-2 agent, build p 2 links involving her. The new agents are by construction order-2 neighbors from agent i 0 ; denote them as class-3 agents. Continue until reaching class-q. This class of trees has two main features: first, any pair of agents in a given class-k, k = 2, 3, • • • , q are symmetric; second, if agent i belongs to class-k and agent j to class-k with k < k , then agent i's degree (i.e. the number of nodes agent i is involved in) is not smaller than that of agent j. For instance, the line network is such that

p 1 = p 2 = • • • = p q = 1
and n = 2q -1. We name this class a hierarchy (see figure 2

-Left).

A definition of centrality for this class. Agents with lower index k have higher centrality.

(for an explanation, see the last remark of the section)

Result 1 For any hierarchy such that p 1 > p 2 , lemma 1 holds.

We omit the detail of the proof. We explain briefly why the lemma still holds (we only mention the part related to the cover configuration). First, we build the cover configuration similarly to the case of the line: recalling that symmetric agents produce the same effort level at any equilibrium, we start with class-1 agent; consider in the rest of the society the set of agents with maximum effort, and among them select one with lowest index. Then put the effort of agents with lower index at this effort level. Replicate the process accordingly until the end of the network. Having built the cover configuration, the proof extends straightforwardly. Consider some agent i belonging to some class-k. Let us suppose that agent i's effort is smaller than one agent say j of class-(k + r) at the equilibrium. Then they produce same effort on the cover configuration. Now it is easy to see that the inflow of agent i is greater than that of agent j on the cover configuration. The networks depicted in figure 3 illustrate the point in the case r = 1 and k > 1. The agents providing externalities to agent i and j can be divided in two separate regions. One region consists in two subtrees of similar pattern: the first contains agent j as top agent and contains the (direct and indirect) descendants of agent j; the second is a replication of this subtree with agent i as top agent. If p k > p k+1 (figure 3-Left), it is sufficient to consider a subtree containing exclusively descendants of agent i; if p k = p k+1 (figure 3-Right), this subtree contains one branch with the class-(k -1) neighbor of agent i. Note that if k = 1, the latter case does not arise since we impose p 1 > p 2 . Then by construction, with any path toward a class-(k + z) descendant of agent j we can associate a path toward a class-(k + z -1) neighbor of agent i, with all efforts of intermediaries greater on the latter path. Using assumptions 1 and 3 is then sufficient to find that agent i receives more inflow than agent j in this region. The complementary region poses no difficulty: decay (assumption 2) basically induces that agent i receives more inflow from this part of the network than agent j. Summing all externalities, we find that agent i receives more inflow than agent j on the cover configuration. Then, starting from the cover configuration, the SBRA would converge to a configuration that dominates the cover configuration.

We remark that the condition p 1 > p 2 is necessary. Indeed, if p 1 = p 2 , the top agent has p 1 direct neighbors while each of her neighbors has p 1 + 1 neighbors (see figure 4).

If decay is strong (a limiting case is when only direct neighbors provide externalities), the top agent may receive less inflow than her neighbors.

Definition. We build the following class of networks. We consider a collection of x identical hierarchies of length say q. Then, we add (i) any symmetric and connected structure between all class-1 agents (a circle, a complete network, • • • ), with average degree d 1 ≥ 1 in this subnetwork; (ii) any symmetric and connected structure between all class-k agents of a same hierarchy, with same average degree d k for all hierarchies.

We impose that d k ≥ d k+1 for k = 1, 2, • • • , q -1. We name this class a hierarchical community (see figure 5). Of course, this class contains hierarchies as defined in the preceding example. The definition of centrality for this class is identical: Agents with lower index k are more central.

On general networks, there may exist more than one path between any pair of agents. Thus, we need to define how we derive some inflow from the collection of paths between two agents. Of course, which function is selected (like max or sum) matters. We restrict attention to functions max (i.e. the externality that agent i receives from agent j is the greatest value over all paths linking them) and sum (i.e. the externality that agent i receives from agent j is the sum of path values over all paths linking them):

Result 2 Suppose that agents receive inflow through either function max or function sum. Any hierarchical community with d 1 ≥ p 2 is such that lemma 1 holds.

Figure 6 illustrates the point with function max. To see why the result holds, build the cover configuration of a symmetric equilibrium as usual. Suppose that agent i is a class-1 agent (which is the case in figure 6). Then d 1 ≥ p 2 guarantees that the equivalent tree to that of descendants of agent j (the red one in figure) can be obtained from agent i (red-doted nodes) with all agents producing more (on the cover configuration) node by node. Considering all paths between pairs of agents, function max ensures that agent i obtains more inflow than agent j on the cover configuration. Now suppose that agent i is not central. Then if p i > p j , only descendants of agent i can be used to find the good tree, and we are done. If p i = p j , then one uses one direct 'parent' of agent i as a source of one branch. Finally, the subnetwork delineated by the doted line and excluding agent i provides either equal inflow to agents i and j, or is favorable to agent i by decay. We do not present the case of function sum; basically it may only increase the difference of inflows in favor of agent i.

Conclusion

This article has studied individual incentives to produce synergic efforts, the returns of which depend on spillovers spreading on a network. In that situation, a social dilemma exists, i.e. some equilibria are Pareto-ranked. First, we provide a characterization of the equilibrium which Pareto-dominates all others, under the form of a simple property (property P ). This characterization holds under general conditions on the propagation of spillovers. Second, this characterization is useful for addressing the issue of social coordination. Considering any equilibrium which is not the most desirable and which does not possess property P , we provide a simple procedure, which exploits property P , to reduce the social dilemma.

Due to the level of generality of our assumptions regarding the transmission of information, our analysis is restricted to specific network architectures, for which centrality ranking is unambiguous. Future research may explore further the relationship between centrality indexes and efforts on more general network architectures, perhaps under more specific decay assumptions. Moreover, the strategic formation of both efforts and links is a challenging issue. Expression (E1): for all k = 1, 2, • • • , k(r) -1, v(p i 0 +r,k ) ≥ v(p i 0 +z(r),k ) by the assumption 2 on decay. Indeed, for all such k, agent i 0 + r is intermediary between agent k and agent i 0 + z(r) on the line. Then we find (E1) ≥ 0. Expression (E2): for each q = 1 to n-i 0 -z(r), v(p i 0 +z(r),i 0 +z(r)+q ) ≤ v(p i 0 +r,i 0 +r-q ) by assumption 1. Assumption 3 therefore predicts that for all such indexes q, v(p i 0 +z(r),i 0 +z(r)+q ) -v(p i 0 +r,i 0 +z(r)+q ) ≤ v(p i 0 +r,i 0 +r-q ) -v(p i 0 +z(r),i 0 +r-q ) Summing all inequalities we obtain (E2) ≥ 0. Expression (E3): By construction of δ H , δ i 0 +r = δ i 0 +r+1 = • • • = δ i 0 +z(r) , so clearly (E3) = 0.

Thus, I H i 0 +r ≥ I H i 0 +z(r) .

(B): Let us apply the SBRA with profile δ H as initial condition ( δ H = δ 0 ), and let δ t denote the value of efforts at the end of round t = 1, 2, • • • . Recall that: every agent in Z produces the same effort level in both configurations δ and δ H , δ is an equilibrium profile, δ H dominates δ, payoff functions satisfy increasing differences.

Then, at the end of the first round of the SBRA, we derive that I H i 0 +z ≥ I i 0 +z for all i 0 + z ∈ Z. Then, by increasing differences property, we have δ 1 i 0 +z ≥ δ H i 0 +z (where superscript '1' quotes here for first round). Now, consider some agent i 0 + r. By (A), I H i 0 +r ≥ I H i 0 +z (r) , where i 0 + z(r) ∈ Z is such that δ H i 0 +r = δ H i 0 +z(r) . Then, the increasing differences property induces that δ 1 i 0 +r ≥ δ 1 i 0 +z (r) . Since δ H i 0 +r = δ H i 0 +z(r) , we have δ 1 i 0 +r ≥ δ H i 0 +r . Hence, all agents increase their efforts at the end of round 1.

Proof of lemma 2. Consider a symmetric configuration δ 0 . Suppose that the configuration δ ∞ it converges to through SBRA does not satisfy property P . Since δ 0H ≤ δ ∞ , we also have δ 0H ≤ δ ∞L , and thus δ 0 ≤ δ ∞L . Now, applying the SBRA with δ 0 and δ ∞L as initial configurations, it is true that for all rounds r ≥ 1, δ r ≤ δ ∞Lr (by increasing difference property). Therefore, δ ∞ ≤ ( δ ∞L ) ∞ (where ( δ ∞L ) ∞ is the configuration the SBRA converges to if we put δ ∞L as initial condition). Remarking that δ ∞ is a symmetric equilibrium, we can apply lemma 1 which says that from the covered configuration of a symmetric equilibrium, SBRA converges toward a configuration dominated by the covered configuration. We find that ( δ ∞L ) ∞ ≤ δ ∞L , inducing finally

δ ∞ ≤ ( δ ∞L ) ∞ ≤ δ ∞L < δ ∞ , a contradiction.

Figure 2 :

 2 Figure 2: A hierarchy (q = 5)

Traditionally, economists conceive two categories of effort spillovers: efforts are either strategic complements or strategic substitutes. In the former (resp. latter) case, more spillovers increase (resp. decrease) incentives to produce effort.

In our analysis, efforts are defined over a compact set of R. Additional results in the context of binary effort choice on the line network are available upon request to the authors.

Interestingly, networks with high level of assortativity in degree are empirically documented in many social network analyses, like the internet network, research collaboration networks, etc.

See Bloch and Dutta (2007), Fery (2007),[START_REF] Hojman | Core and Periphery in Endogenous Networks[END_REF],[START_REF] Matsubayashi | A note on network formation with decay[END_REF] Yamakawa (2006), Rogers (2005).

The 'strict' refinement means that no Nash equilibrium contains two agents with same inflow and different effort levels.

Every agent i ∈ N has a unique symmetric agent, who is agent n -i + 1.

APPENDIX: PROOFS

Proof of lemma 1. Suppose that a symmetric equilibrium δ does not satisfy property P . if a SBRA starts from its cover (resp. covered) configuration δ H , all agents produce a higher (resp. lower) effort level after round 1.

Denote i 0 the index of the central agent:

Considering one symmetric equilibrium δ and its cover configuration δ H , we define the set

In words, the set Z contains agents such that their effort level on the cover configuration is the same as their effort in the equilibrium configuration δ, and such that their less central neighbor produces a strictly lower effort on the cover configuration.

Part (A) shows that, in the cover configuration δ H , if we have two agents, say i and j, with same effort level and such that agent i ∈ Z while j / ∈ Z (then agent j is more central than agent i by construction of Z), then agent i receives a lower inflow.

Part (B) shows that the SBRA converges to a configuration which dominates δ.

(A): Recall that δ H is symmetric. Fix, in δ H , any agent i 0 + r, r ≥ 0. Consider the r) (superscript H quotes here for the effort in profile δ H ). Note that r ≤ z(r). Having fixed r, Let k(r) = 2i 0 + r -(n -z); agent k(r), placed at the left side of agent i 0 + r, is such that (i 0 + r) -k(r) = n -(i 0 + z(r)). Note that k(r) > 1 if r > 0. Writing the difference I H i 0 +r -I H i 0 +z(r) and rearranging, we find:


Tangi Aubert

Alexandra Y Ledneva

Fabien Grasset
email: fabien.grasset@univ-rennes1.fr.

Koji Kimoto

Nikolay G Naumov

Yann Molard

Noriko Saito

Hajime Haneda

Stéphane Cordier
email: stephane.cordier@univ-rennes1.fr.

L = Oh

St Ephane Cordier

Synthesis and characterization of A4[Re6Q8L6]@SiO2 red-emitting silica nanoparticles based on Re6 metal atom clusters (A = Cs or K, Q = S or Se

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

Introduction

Many solid-state compounds, hybrid assemblies, and nanomaterials are based on octahedral metal atom clusters (M 6 , with M = Mo, W, and Re) characterized by metal-metal bonds. 1,2 The M 6 cluster is surrounded by eight face-capping ligands (L i , i = inner) to form a rigid M 6 Y i 8 core that is coordinated to six terminal ligands (L a , a = apical) leading to an M 6 Y i 8 X a 6 neutral or anionic unit (Y = chalocogen and/or halogen; X = halogen).

Solid-state materials based on such M 6 Y i 8 X a 6 units are easily synthesized at high temperature. They have been studied for many years for their interesting transport, catalytic, and electronic properties. [3][4][5][6][7] Many routes now afford soluble inorganic cluster precursors for soft chemistry synthesis. 8,9 Indeed, owing to their nanosized shape and their structural, redox, and photoluminescence properties, M 6 Y i 8 X a 6 anionic units constitute relevant building 38 blocks for the elaboration of supramolecular assemblies, nano-39 materials, and functionalized surfaces. [10][11][12][13][14][15][16][17][18][19][20][21] In solution or in inorganic 40 (or organic) melts, apical ligands can be replaced by other ligands 41 that are not stable under the synthesis conditions of the cluster. 42 For instance, the reaction between Cs 3 [Re 6 Q 7 Br 7 ] 3 H 2 O (Q = S 43 or Se) and melted pyrazine (pyz) leads to the formation of fac-

44

[Re 6 Q i 7 Br i (pyz) a 3 Br a 3 ] 3 xH 2 O units that self-assembly via supra-In addition to applications in biotechnology, functional silica 75 particles can also find numerous applications in a wide range of 76 fields such as photonics, 40 catalysis, 41 data storage devices, 42 cos-77 metics, 43 and so forth. In this article, we report the preparation of . The whole cluster unit is roughly 1 nm in size, depending on the nature of the apical ligands, and is negatively charged; it therefore needs to be charge balanced by counter cations in the solid state (here Cs or K). Most of the clusters are prepared by gas-solid or solid-solid synthesis and generally at high temperature. The cluster precursors used in this study were prepared according to well-known procedures reported in the literature. [45][46][47] They are briefly described in this section and summarized in Scheme 1

S1

. 48,49 144 or hexamolybdenum clusters in silica nanoparticles, 30 and this is 145 illustrated in Figure 2 F2 . For all of the syntheses described here, the 146 quantities of precursors used to form the final mixture were the 147 following: 47 mL of heptane, 15 mL of Brij30, 1.6 mL of an aqueous cluster sol, 1.3 mL of ammonia, and 2 mL of TEOS. To create the microemulsion, heptane (oil phase) was first mixed with Brij30 (surfactant), and then an aqueous ammonia solution and an aqueous cluster sol were slowly added to the mixture. The aqueous cluster sol was obtained simply by solubilization of the cluster precursor in water. Depending on the solubility, the cluster concentration in the final aqueous phase could be adjusted. For

Characterization of Materials.

The external morphology of the nanoparticles was studied by field emission scanning electron microscopy (FE-SEM) with a Hitachi SU8000 working at an acceleration voltage of 10 kV. For FE-SEM observations, the nanoparticles were deposited on a silicon wafer and coated with a 3 nm layer of platinum using a JEOL JFC-1600 auto fine coater to enhance the conductivity of the sample. The microstructure of the nanoparticles and the distribution of the cluster units were observed using a scanning transmission electron microscope (Hitachi High-Technologies, HD-2300C) equipped with a spherical aberration corrector (CEOS GmbH, CESCOR) and working in annular dark-field mode (ADF-STEM). 50,51 The acceleration voltage was 200 kV, the convergent semiangle was 27.5 mrad, and the inner angle of the annular dark-field detector was 80 mrad. The spatial resolution of the instrument was about 0.1 nm. For ADF-STEM observation, the nanoparticles were dispersed on a thin carbon film whose thickness was about 6 nm.

Investigations of the photoluminescence properties were performed in the solid state with a Jobin Yvon Fluorolog-3 fluorescence spectrometer (FL3-22, Horiba Jobin Yvon). The vibrational spectra were recorded with a Raman Bruker IFS 28 spectrometer equipped with a FRA 106 module. The excitation source was provided by a Nd:YAG laser working at 1064 nm. The power of the 44 For the preparation of A 4 [Re 6 Q 8 L 6 ]@SiO 2 nanoparticles, the cluster precursors were initially dissolved in water. Then, to prevent any change in the luminescence properties and to avoid precipitation of the clusters due to low pH, the microemulsions were prepared by adding ammonia to the heptane/Brij30 mixture prior to the aqueous cluster sol and prior to TEOS, so both the hydrolysis and condensation steps in the silica synthesis were base-catalyzed. The nanoparticles were then prepared according to the procedure described in section 2.3.

Nanoparticle Morphology and Microstructure.

The as-prepared nanoparticles were observed by FE-SEM. The image analyses of A 4 [Re 6 Q 8 L 6 ]@SiO 2 nanoparticles (Figure 3 F3 ) showed that they all exhibit a perfectly spherical, monodisperse morphology with an average diameter of 30 nm for the synthesis conditions described in section 2.3. Supplementary experiments showed that the size of the nanoparticles does not depend on the cluster concentration in the aqueous phase. To study the microstructure of the nanoparticles and confirm the encapsulation of the cluster units, the ADF-STEM technique is the only suitable tool because of the size of the cluster units (1 nm). Indeed, by detecting electrons scattered at high angles this technique provides what is known as Z-contrast images because atoms with high atomic numbers will be more scattered at high angle than atoms with lower atomic numbers. Thus, thanks to the large difference in electron numbers between the Re cluster core and Si or O from the silica matrix and the high spatial resolution of the STEM, it was possible to visualize the cluster units inside the nanoparticles. For example, Figure 4 F4 shows an ADF-STEM image of K 4 [Re 6 S 8 -(OH) 6 ]@SiO 2 nanoparticles where cluster units are visible as bright spots of about 1 nm in size. This image confirms that precursor to 700 nm after embedding in the silica matrix (Figure 5d).

A closer look at the emission spectra shows that the shape of the emission spectrum of Cs 4 [Re 6 S 8 Br 6 ]@SiO 2 nanoparticles (Figure 5d)

and that of K 4 [Re 6 S 8 (OH) 6 ]@SiO 2 nanoparticles (Figure 5b) SiO 2 (Figure 5b). This finding again indicates that -Br apical ligands of [Re 6 S 8 Br 6 ] 4-cluster units might be substituted for -OH groups during the microemulsion process.

The luminescence of clusters is usually quenched in solution because of the presence of solubilized oxygen. Indeed, it has been known for many years that excited octahedral clusters can be relaxed through the creation of singlet oxygen. [START_REF] Chevrel | Chemistry and Structure of Ternary Molybdenum Chalcogenides[END_REF] This quenching effect was successfully prevented by embedding the cluster units in silica nanoparticles. For illustration, Figure 6 F6 shows a comparison between the luminescence properties of [Re 6 S 8 (OH) 6 ]

  78 novel NIR-emitting nanoparticles obtained by the encapsulation 79 of [Re 6 Q 8 L 6 ] 4-cluster units (Q = S or Se and L = OH or CN) in 80 silica nanoparticles by an adapted microemulsion process. Several 81 kinds of clusters have been used to study the influence of the 82 nature of inner and apical ligands on the cluster-embedding 83 process as well as on the luminescence properties of embedded 84 clusters. The Re 6 cluster precursors involved in this work were K 4 [Re 6 Q 8 (OH) 6 ] (Q = S or Se), Cs 4 [Re 6 S 8 Br 6 ], and Cs 1.68 K 2.32 -[Re 6 S 8 (CN) 4 (OH) 2 ]. These Re 6 clusters are all luminescent in the red and NIR fields, with luminescence lifetimes of a few microseconds depending on the ligands.

F1

Figure 1 .

 1 Figure 1. Schematic representation of a Re 6 Q i 8 L a 6 cluster unit. The Re 6 cluster core is represented as a gray octahedron. Inner ligands (Q i = S or Se) are in the face-capping position, and apical ligands (L a = OH, CN or Br) are in terminal positions.

K 4 [

 4 Re 6 S 8 (OH) 6 ] and K 4 [Re 6 Se 8 (OH) 6 ], this concentration was limited to 5 mM whereas it could reach 16 mM for Cs 4 [Re 6 S 8 Br 6 ] and 25 mM for Cs 1.68 K 2.32 [Re 6 (CN) 4 (OH) 2 ]. Once the microemulsion became a clear, stable solution, the silica precursor (TEOS) was added for the synthesis of the silica shell that occurred directly inside the aqueous nanodroplets already containing the cluster units. After the addition of TEOS, the reaction was stirred for 3 days and then the microemulsion was destabilized with ethanol and the nanoparticles were washed twice with an ethanol/heptane mixture (3:1 volume ratio) by centrifuging at 5000 rpm. Note that before destabilization of the microemulsion, the nanoparticle surface can be easily functionalized by the addition of a functional organosilane precursor. Finally, the nanoparticles could be either redispersed in solution (water or ethanol) or dried in ambient air.

Scheme 1 .

 1 Scheme 1. Summary of the Synthesis of Re 6 Inorganic Cluster Precursors a

Figure 2 .A 4 [ 3 .Cs 2 [

 2432 Figure 2. Schematic representation of the microemulsion process for the encapsulation of rhenium clusters inside a silica nanoparticle.

Figure 3 .

 3 Figure 3. FE-SEM pictures of (a) K 4 [Re 6 S 8 (OH) 6 ]@SiO 2 and (b) Cs 1.68 K 2.32 [Re 6 S 8 (CN) 4 (OH) 2 ]@SiO 2 nanoparticles.

Figure 4 .

 4 Figure 4. ADF-STEM pictures of K 4 [Re 6 S 8 (OH) 6 ]@SiO 2 nanoparticles with discrete cluster units (bright spots).

3. 3 .

 3 Luminescence Properties. The successful encapsulation of the cluster units in the silica nanoparticles was also evidenced by studying the luminescence properties of A 4 [Re 6 Q 8 L 6 ]@SiO 2 nanoparticles. The luminescence properties were investigated in the solid state for both the A 4 [Re 6 Q i 8 L a 6 ] cluster precursors and the corresponding A 4 [Re 6 Q 8 L 6 ]@SiO 2 nanoparticles. In Figure5F5 , the excitation and emission spectra for each type of cluster are plotted, and in Table1

T1,

  the wavelength values at the emission maximum (λ em ) are summarized. The encapsulation of the [Re 6 Q i 8 (OH) a 6 ] 4-(Q = Se or S) and [Re 6 S i 8 (CN) a 4 (OH) a 2 ] 4-cluster units in the silica matrix resulted in a slight shift of the emission maxima after embedding, but the shape of the emission spectrum remained unchanged (Figure 5a-c). The emission maxima shifts, ranging from 10 to 20 nm, to higher wavelengths between solid-state precursors and the nanoparticles must be due to some perturbations of the molecular orbital diagram of [Re 6 Q i 8 L a 6 ] 4-units after embedding. One could suspect a slight decrease in the energy gap between excited and fundamental states. Some questions arose concerning the embedding of [Re 6 S i 8 Br a 6 ]4- units in silica nanoparticles. Indeed, the emission maxima for [Re 6 S i 8 Br a 6 ] 4-units decreased from 800 nm in the Cs 4 [Re 6 S 8 Br 6 ]

  292 match perfectly. This drastic change between the luminescence 293 properties of the starting and embedded clusters can then be 294 explained by an exchange of -Br apical ligands for -OH groups 295 during the microemulsion process. In an attempt to avoid this 296 structural modification, another synthesis of Cs 4 [Re 6 S 8 Br 6 ]@ 297 SiO 2 nanoparticles was performed using acidic cluster sols (in which 298 the pH was adjusted to 2 with HBr) either in a pure water solution 299 or in a water/ethanol mixture (1:1 v/v). In both cases, the micro-300 emulsion stability was not affected but the resulting nanoparticles 301 still show a luminescence shift to lower wavelengths, probably as a

Figure 5 .

 5 Figure 5. Normalized excitation and emission spectra (corrected signals) for both A 4 [Re 6 Q 8 L 6 ] cluster precursors (---) and A 4 [Re 6 Q 8 L 6 ]@ SiO 2 nanoparticles (-) for (a) K 4 [Re 6 Se 8 (OH) 6 ], (b) K 4 [Re 6 S 8 (OH) 6 ], (c) Cs 1.68 K 2.32 [Re 6 S 8 (CN) 4 (OH) 2 ], and (d) Cs 4 [Re 6 S 8 Br 6 ].

Figure 6 .

 6 Figure 6. Aqueous solution of [Re 6 S 8 (OH) 6 ] 4-clusters (a) before and (b) after embedding in silica nanoparticles, under daylight (left picture) and under UV irradiation at 365 nm (right picture).

Figure 7 .

 7 Figure 7. Raman spectra for both A 4 [Re 6 Q 8 L 6 ] cluster precursors (---) and A 4 [Re 6 Q 8 L 6 ]@SiO 2 nanoparticles (-) for (a) K 4 [Re 6 Se 8 (OH) 6 ], (b) K 4 [Re 6 S 8 (OH) 6 ], (c) Cs 1.68 K 2.32 [Re 6 S 8 (CN) 4 (OH) 2 ], and (d) Cs 4 [Re 6 S 8 Br 6 ].

Cs 4 [Re 6 S 8 Br 6 ]. 47 Cs 4 [Re 6 S 8 Br 6 ] was prepared by the 131 reaction of K 4 [Re 6 S 8 (OH) 6 ] with CsBr in a water solution and 132 with the pH adjusted to 2 with HBr. 133 2.2.3. Cs 1.68 K 2.32 [Re 6 S 8 (CN) 4 (OH) 2 ]. 46 ReS 2 was prepared 134 by the reaction of Re with S under vacuum at 450 °C for 2 days.

  ). This binary compound was then mixed with KOH Cs 1.68 K 2.32 [Re 6 S 8 (CN) 4 (OH) 2 ] was obtained by the reac-138 tion of Cs 4 [Re 6 S 9 (CN) 4 ] with KOH in water, which had been Synthesis of A 4 [Re 6 Q 8 L 6 ]@SiO 2 Nanoparticles.

	128	and held at 200 °C (or 280 °C, respectively) in ambient air to
	129	obtain K 4 [Re 6 Se 8 (OH) 6 ] (or K 4 [Re 6 S 8 (OH) 6 ], respectively).
	130 2.2.2. 135 Cs 4 [Re 6 S 9 (CN) 4 ] was then synthesized by the reaction of ReS 2 136 with KCN in the presence of excess CsCl at 650 °C for 48 h. 45
	137 Finally, 139 boiled for 24 h.
	141	The A 4 [Re 6 Q 8 L 6 ]@SiO 2 nanoparticles were prepared through a
	142	microemulsion process adapted from a previously reported synthe-
	143	sis for the encapsulation of nanocrystals (CeO 2 or ZnFe 2 O 4 )

140 2.3.

Table 1 .

 1 Emission Maximum Wavelengths (λ em ) for A 4 [Re 6 Q 8 L 6 ] Cluster Precursors and A 4 [Re 6 Q 8 L 6 ]@SiO 2 Nanoparticles A 4 [Re 6 Q 8 L 6 ] cluster precursor λ em (nm) A 4 [Re 6 Q 8 L 6 ]@SiO 2 nanoparticles λ em (nm)

	K 4 [Re 6 S 8 (OH) 6 ]	680	K 4 [Re 6 S 8 (OH) 6 ]@SiO 2	700
	K 4 [Re 6 Se 8 (OH) 6 ]	675	K 4 [Re 6 Se 8 (OH) 6 ]@SiO 2	690
	Cs 1.68 K 2.32 [Re 6 S 8 (CN) 4 (OH) 2 ]	750	Cs 1.68 K 2.32 [Re 6 S 8 (CN) 4 (OH) 2 ]@SiO 2	760
	Cs 4 [Re 6 S 8 Br 6 ]	800	Cs 4 [Re 6 S 8 Br 6 ]@SiO 2	700

  Re 6 Q 8 L 6 ]@SiO 2 nanoparticles and are 348 respectively attributed to the T 2g vibrational mode and the A 1g -349 symmetric S 8 breathing mode of the clusters. For Cs 1.68 K 2.32 -350 [Re 6 S 8 (CN) 4 (OH) 2 ]@SiO 2 , another strong peak is easily identifi-351 able at 2120 cm -1 (data not shown here), which is due to the A 1g 352 vibrational mode of the CN groups. Concerning K 4 [Re 6 Se 8 -353 (OH) 6 ]@SiO 2 nanoparticles (Figure 7a), the two intense peaks 354 at 200 and 260 cm -1 can be observed and attributed to the T 2g and 355 Se 8 -A 1g vibrational modes, respectively, although they are slightly 356 shifted (about 10 cm -1 ) compared to the corresponding peaks in 357 the starting cluster precursor. The spectra of K 4 Re 6 Se 8 (OH) 6 @ 358 SiO 2 , K 4 Re 6 S 8 (OH) 6 @SiO 2 , and Cs 1.68 K 2.32 [Re 6 S 8 (CN) 4 (OH) 2 ]@ Br 6 ]@SiO 2 nanoparticles does not fully agree with the 364 Raman signature of the Cs 4 [Re 6 S 8 Br 6 ] cluster precursor. Actu-365 ally, the shape of the Raman spectrum for Cs 4 [Re 6 S 8 Br 6 ]@SiO 2 366 nanoparticles (Figure7d) is similar to the spectrum of the 367 K 4 [Re 6 S 8 (OH) 6 ]@SiO 2 nanoparticles (Figure7b). Moreover, in

		modes.	342
		The Raman spectra of the cluster precursors and of the	343
		corresponding cluster-based silica nanoparticles are represented	344
		in Figure 7 . For all of the sulfide derivates (Figure 7b-d), the	345	F7
		strong peaks at 280 and 430 cm -1 are easily identifiable in spectra	346
	4-	347 of corresponding A 4 [359 SiO 2 nanoparticles exhibit all of the typical Raman signatures of 360 the corresponding cluster precursor. This consequently confirms
	cluster units in a water solution and after being embedded in	the successful encapsulation of the cluster units without signifi-	361
	silica nanoparticles under normal light and under UV irradiation at 365 nm. The [Re 6 S 8 (OH) 6 ] 4-clusters show luminescence only	cant structural modification. In contrast, the spectrum of Cs 4 -[Re 6 S 8	362 363
	when they are embedded in the silica matrix because they are then
	protected from the presence of solubilized oxygen and their
	luminescence is no longer quenched.
	3.4. Raman Study. The vibrational properties of the A 4 -
	[Re 6 Q 8 L 6 ] cluster precursors and those of A 4 [Re 6 Q 8 L 6 ]@SiO 2
	nanoparticles were investigated by Raman spectroscopy. The
	characterization of M 6 Q i 8 L a 6 units by Raman spectroscopy is

not usual. The few published results show typical vibrations in the 50 to 400 cm -1 region. Their assignment is particularly tricky when the symmetry of the M 6 Q i 8 L a 6 units deviates from O h 338 symmetry. On the basis of the experimental and theoretical 339 Raman investigations performed on Re 6 Q i 8 L a 6 -cluster-unit-340 based compounds by Gray et al., 57 it turns out that the Raman 341 bands correspond to different kinds of L a 6 , Q i 8 , and Re 6 breathing 368 Figure 7d the two intense peaks at 140 and 160 cm -1 , which were 369 attributed to Re-Br a vibrational modes by Gray et al., are clearly

Acknowledgment. This work was supported by the University of Rennes 1, CNRS, and joint Japan-RFBR grant 09-03-92100-R Φ_a. Christiane Perrin is acknowledged for helpful discussions and local management of the PECO-NEI & ECONET programs. A.Y.L. and N.G.N. are grateful to the PECO-NEI & ECONET programs for research grants at the University of Rennes 1. T.A. thanks R egion Bretagne for a Ph.D. grant and the Coll ege Doctoral Franco-Japonais for a research grant at NIMS. We thank Dr. K. Hasegawa (NIMS) for supplying the SEM images and Dr. F. Paul (University of Rennes 1) for the Raman measurements.

nm in size with good monodispersity and exhibit a perfectly 387 spherical shape. The cluster units are homogeneously dispersed inside the nanoparticles. A very important feature is that when embedded in silica the luminescence of the clusters is not quenched by oxygen in solution.

Toxicological studies are currently performed to evaluate the toxicological potential of such nanoparticles. If the silica shell efficiently proves to prevent any toxic effect from the metal atom clusters, then such material will have numerous potential applications in the field of biotechnology.