Laura Marcela

Forero Ramirez

Jérôme Babin

Ariane Boudier

Caroline Gaucher

Marc Schmutz

Mériem Er-Rafik

Alain Durand

Jean-Luc Six

Cécile Nouvel
email: cecile.nouvel@univ-lorraine.fr

First multi-reactive polysaccharide-based transurf to produce potentially biocompatible dextran-covered nanocapsules

Keywords:

A multi-reactive polysaccharide-based transurf (acting both as macro-Chain Transfer Agent and stabilizer) was used to confine RAFT polymerization of methyl methacrylate (MMA) at the oil/water (o/w) miniemulsion interface. Dithiobenzoate groups and hydrophobic aliphatic side chains were introduced onto dextran, conferring it both transfer agent properties and ability to stabilize direct miniemulsion of MMA in the presence of a biocompatible oil, used as co-stabilizer. Because of their amphiphilic character, transurfs were initially adsorbed at the (o/w) interface and their reactive sites mediated RAFT polymerization via the R-group approach. PMMA-grafted dextran glycopolymers were consequently produced at the o/w interface, thus leading to dextran coverage/PMMA shell/oily core nanocapsules (NCs) as evidenced by Cryo-TEM analyses. The influence of dextran-based transurf chemistry and oil amount on MMA RAFT polymerization control was investigated. Positive preliminary results

on NCs cytotoxicity suggest the potential of these objects for biomedical applications.

Introduction

Polymer nanocapsules (NCs) have attracted greater attention in recent years because of their unique properties and potential applications in the biomedical field, for instance as drug delivery systems [START_REF] Mora-Huertas | Polymer-based nanocapsules for drug delivery[END_REF][START_REF] Vrignaud | Strategies for the nanoencapsulation of hydrophilic molecules in polymer-based nanoparticles[END_REF][START_REF] Poltorak | Interfacial click chemistry for improving both dextran shell density and stability of biocompatible nanocapsules[END_REF][START_REF] Six | Polymerization induced self-assembly: an opportunity toward the self-assembly of polysaccharide-containing copolymers into high-order morphologies[END_REF]. Miniemulsion polymerization is a promising technique that allows drug encapsulation and NCs production in one-pot [START_REF] Steinmacher | Kinetics of MMA and VAc Miniemulsion Polymerizations Using Miglyol and Castor Oil as Hydrophobe and Liquid Core[END_REF]. To produce oily-core NCs by this technique, nanodroplets with size ranging from 50 to 500 nm are initially obtained by dispersion of a monomer/oil mixture in an aqueous phase. Nanodroplets are protected against coalescence by the presence of stabilizer and preserved from Ostwald ripening by the addition of an osmotic pressure agent (co-stabilizer), which may be the oil constituting the inner liquid core in the final NCs [START_REF] Steinmacher | Kinetics of MMA and VAc Miniemulsion Polymerizations Using Miglyol and Castor Oil as Hydrophobe and Liquid Core[END_REF][START_REF] Landfester | Nanocapsules with specific targeting and release properties using miniemulsion polymerization[END_REF][START_REF] Ramirez | Multi-reactive surfactant and miniemulsion Atom Transfer Radical Polymerization: An elegant controlled one-step way to obtain dextran-covered nanocapsules[END_REF]. In such a case, oily core and polymeric shell will be formed during polymerization by means of induced-phase separation whereby polymer migrates to the droplet/water interface due to poor solubility in the oil. However, a well-defined core/shell structure can be difficult to obtain because of the strict thermodynamic and kinetic parameters involved in polymer/oil separation. Moreover, stabilizers are usually physically adsorbed at NCs surface and can be easily removed or replaced by surface-active molecules present in physiological media, which may thus affect the colloidal stability or enhance unwanted immune responses.

To overcome all the above limitations, some authors reported the combination of monoreactive amphiphilic copolymers as miniemulsion stabilizers with Reversible-Deactivation Radical Polymerizations (RDRP) such as Atom Transfer Radical Polymerization (ATRP) or Reversible Addition-Fragmentation chain Transfer (RAFT) polymerization to confine polymerization at the oil/water interface. While keeping their role as stabilizers, these copolymers acted either as mono-reactive inisurfs (initiators and stabilizers) [START_REF] Li | Reactive Surfactants for Polymeric Nanocapsules via Interfacially Confined Miniemulsion ATRP[END_REF][START_REF] Li | Dual-Reactive Surfactant Used for Synthesis of Functional Nanocapsules in Miniemulsion[END_REF][START_REF] Tian | Synthesis of multifunctional nanocapsules via interfacial AGET ATRP in miniemulsion for tumor microenvironment responsive drug delivery[END_REF] or transurfs (transfer agents and stabilizers) [START_REF] Luo | Nanoencapsulation via interfacially confined reversible addition fragmentation transfer (RAFT) miniemulsion polymerization[END_REF][START_REF] Lu | pH Effects on the Synthesis of Nanocapsules via Interfacial Miniemulsion Polymerization Mediated by Amphiphilic RAFT Agent with the R Group of Poly(methyl acrylic acidran -styrene)[END_REF][START_REF] Yu | Comparison of styrene reversible addition-fragmentation chain-transfer polymerization in a miniemulsion system stabilized by ammonlysis poly(styrene-alt-maleic anhydride) and sodium dodecyl sulfate[END_REF]. This strategy was shown to offer several advantages. Firstly, polymer chains grow directly at, or in the proximity of the interface thus allowing formation of polymeric shell at the droplet periphery. Secondly, the stabilizer provides a permanent hydrophilic covalently-linked coverage in the final NCs. Thirdly, the use of ATRP or RAFT polymerization offers the possibility of precise control of macromolecular parameters of the polymeric shell. With similar objectives, our team recently reported the first multi-reactive dextran-based inisurf used in ATRP polymerization of butyl acrylate [START_REF] Wu | First multi-reactive dextran-based inisurf for atom transfer radical polymerization in miniemulsion[END_REF] and of methyl methacrylate (MMA) [START_REF] Ramirez | Multi-reactive surfactant and miniemulsion Atom Transfer Radical Polymerization: An elegant controlled one-step way to obtain dextran-covered nanocapsules[END_REF]. In such cases, grafted dextranbased copolymers were synthesized leading to nanoparticles (NPs) with covalently-anchored hydrophilic dextran coverage. This coverage is expected to enhance NPs biocompatibility as well as to ensure their colloidal stability and stealthiness, while offering the opportunity to further functionalize their surface. Nevertheless, this ATRP process requires additional purification steps to remove remaining copper catalysts after polymerization. We herein hypothesize that switching ATRP to RAFT polymerization (Scheme 1) will overcome this issue and will lead to the production of more suitable NCs for biomedical applications. This new approach required the synthesis of a novel dextran derivative (transurf) carrying hydrophobic and chain transfer agent (CTA) groups and acting as stabilizer and macro-CTA during the miniemulsion process. To the best of our knowledge, it is the first time that RAFT polymerization has been performed in a miniemulsion using a multi-reactive macro-CTA and the above described dextran-based transurf is the second example thereof. In fact, one monoreactive dextran-based macro-CTA was previously reported for vinyl acetate polymerization in emulsion, but the transurf was only formed during the polymerization process [START_REF] Bernard | Preparation of a xanthateterminated dextran by click chemistry: Application to the synthesis of polysaccharide-coated nanoparticles via surfactant-free ab initio emulsion polymerization of vinyl acetate[END_REF]. Moreover, among all the works dealing with the use of transurfs in miniemulsion polymerization, the production of oily-core NCs is scarcely related, and the preparation of PMMA-shell NCs has never been approached, which contributes to the originality of the present work.

Herein, we hypothesize that using a dextran-based multi-reactive transurf can help to produce oily-core/PMMA shell NCs by RAFT interfacial miniemulsion polymerization Transurfs were first designed with a precise control of hydrophobic and CTA groups numbers to provide convenient stabilizing and transfer agent properties. After model studies on MMA polymerization, RAFT polymerization of MMA in miniemulsion was carried out using such dextran-based transurfs: polymerization kinetics, molar mass control and CTA groups' efficiency were studied. Detailed characterization of NCs in terms of size distribution, amount of dextran at the surface, morphology and cytotoxicity were performed to prove the formation of oily-core NCs, usable as platform for drug delivery.

Scheme 1. Synthesis of dextran-covered oily-core NCs by MMA RAFT polymerization in miniemulsion

Materials and methods

Materials

Dextran T40 ( = 26 000 g/mol, Đ = 1.3; values determined by size exclusion chromatography coupled to a multi-angle laser light scattering detector (SEC-MALLS) in DMSO/NaNO3 (0,1 M)) was purchased from Aldrich. Produced from Leuconostoc mesenteroides B 512-F, it was having very low branching (< 5% as given by the furnisher).

Consequently, it could be considered as linear. MMA (99% Aldrich) was vacuum distilled from CaH2. 2,2-Azobis(isobutyronitrile) (AIBN, 99%, Aldrich) was purified by recrystallization from methanol. All those were used without further purification: N-(3dimethylaminopropyl)-N′-ethylcarbodiimide hydrochloride (EDC, 99%, ABCR), 4-(dimethylamino)pyridine (DMAP, 99%, Aldrich), carbonyldiimidazole (CDI, 99%, Aldrich), 2-cyanoprop-2-yl dithiobenzoate (CPDB, >97%, Aldrich), 4-cyanopentanoic acid dithiobenzoate (CPADB, >97%, Aldrich). Miglyol ® 810 (M810, d = 0.94 g/cm 3 , viscosity = 28 mPa.s at 20°C, water content = 0.02 wt%) was a gift from CREMER Oleo GmbH & Co.

Division. M810 belonged to triacylglycerols (also called triglycerides) and was made from a mixture of saturated fatty acids (mainly caprylic acid -69.3 wt%-and capric acid -30.1 wt%), giving it a log P value of 10.2 as evaluated by group contribution methods (Ramirez, Babin, Durand, Six, & Nouvel, 2015).

Transurf synthesis

The transurf was synthesized in two steps. In the first step, the attachment of azide endfunctionalized side chains onto dextran was performed in DMSO by reaction of 6azidohexanoic acid activated with carbonyldiimidazole as previously described leading to DexN3-derivatives [START_REF] Laville | Polysaccharide-covered nanoparticles with improved shell stability using clickchemistry strategies[END_REF]. In the second step, introduction of dithiobenzoate CTA groups was performed using classic EDC/DMAP catalyzed esterification and DexN3-CTA transurfs were obtained (see Supporting Information). and correspond to the number of N3-end alkyl chains (N3) and dithiobenzoate CTA groups per 100 glucopyranosic units, respectively, (i. e. Substitution Degrees) and were estimated by 1 H NMR in DMSO-d6 using equations 1 and 2 (Figure 1). 3 corresponds to the area of 6 methylene protons of alkyl chains (1.2 to 1.7 ppm), is the area of the 5 aromatic protons of dithiobenzoate groups (7.4 to 8.1 ppm) and (4.3 to 5.2 ppm) corresponds globally to 4 protons per glucopyranosic unit, whatever the modification yield. The chemical shift of protons "f" was equal to 3.3 ppm, according the 1 H NMR spectrum of the 6-azidohexanoic acid in DMSO-d6 (not shown).

RAFT polymerization of MMA in miniemulsion

Typical experimental conditions were as follows: [DexN3-CTA ]0 = 10 g/L, DexN3-CTA /organic phase (MMA + M810) was varied from 13 to 36 wt% and M810/MMA from 10 to 50 vol.%. [CTA groups]0/[AIBN]0 molar ratio was fixed to 3. For example, in case of DexN3-20CTA3.7 transurf and M810/MMA = 10 vol.% (Run 1, Table 1), DexN3-20CTA3.7/organic phase (MMA + M810) was 13.2 wt%. 150 mg of DexN3-20CTA3.7 were dissolved in 15 mL of MilliQ water. The organic phase was composed of 1.1 mL (10.3 mmol) of MMA, 110 µL of M810 and 1.3 mg (7.9x10 -3 mmol) of AIBN. The aqueous phase was poured into this organic phase and the mixture was sonicated in an ice bath during 2 min (51% amplitude (power 46 W), pulsed mode) using a Vibracell 600W (Sonics & Materials, Dantbury, CT). Droplets size of the resulting miniemulsion was measured immediately after sonication. The miniemulsion was then transferred to a Schlenk tube covered with a 3-way stopcock and purged with a little nitrogen flow during 45 min at 10 °C. The reactor was then immersed in a thermostatted oil bath at 80 °C to start polymerization. To follow reaction kinetics and evolution of molar masses and particles size, the resulting suspensions were divided in three parts. The first one was kept apart for size measurements. The second one was used to determine monomer conversion (x) by a gravimetric method after vacuum drying for 24 hours. NCs were washed twice with THF then dried to obtain the grafted glycopolymers named DexN3--g-$ % & , where n is the number of PMMA grafts (having an average molecular weight equal to ' ) per 100 glucopyranosic units, respectively.

In order to study PMMA grafts, the dextran backbone of such glycopolymers was completely degraded under basic conditions as previously reported [START_REF] Dupayage | PMMAgrafted dextran glycopolymers by atom transfer radical polymerization[END_REF]. The uncoupled PMMA grafts were analyzed by 1 H NMR in DMSO-d6

to verify the absence of dextran backbone. Their molar masses were then characterized by SEC-MALLS in THF. The remaining suspension was centrifuged. Recovered NCs were washed twice and dispersed in deionized water for biological tests, whereas the floating was analyzed by anthrone titration [START_REF] Wu | First multi-reactive dextran-based inisurf for atom transfer radical polymerization in miniemulsion[END_REF] to estimate the quantity of DexN3-CTA remaining in aqueous solution. By difference with the initially introduced amount, one can estimate the quantity of dextran derivative adsorbed at the NC surface. Microscopy (cryo-TEM) as reported [START_REF] Ramirez | Multi-reactive surfactant and miniemulsion Atom Transfer Radical Polymerization: An elegant controlled one-step way to obtain dextran-covered nanocapsules[END_REF].

Characterization

SEC-MALLS analyses of PMMA chains were performed in THF at 40 o C. Refractive index increment (dn/dc) of 0.087 mL.g -1 was used (See Supporting Information).

NCs cytocompatibility was evaluated on rat vascular smooth muscle cell line (A-10, ATCC_ CRL-1476™) (See Supporting Information).

Results and discussion

DexN3-CTA transurf

To the best of our knowledge, relatively few examples of polysaccharides bearing RAFT functionality have been described in the literature and only 4 examples were based on dextran.

One xanthate-end functionalized dextran RAFT agent was prepared by click chemistry [START_REF] Bernard | Preparation of a xanthateterminated dextran by click chemistry: Application to the synthesis of polysaccharide-coated nanoparticles via surfactant-free ab initio emulsion polymerization of vinyl acetate[END_REF] and three multi-reactive dextran-based macro-CTA were obtained by esterification [START_REF] Duong | Functionalizing Biodegradable Dextran Scaffolds Using Living Radical Polymerization: New Versatile Nanoparticles for the Delivery of Therapeutic Molecules[END_REF][START_REF] Ferji | In situ glyco-nanostructure formulation via photo-polymerization induced self-assembly[END_REF][START_REF] Karmakar | Synthesis of RAFT-Mediated Amphiphilic Graft Copolymeric Micelle Using Dextran and Poly (Oleic Acid) toward Oral Delivery of Nifedipine[END_REF]. Nevertheless none of them was also used as stabilizer in miniemulsion polymerization.

Herein, the first multi-reactive dextran-based transurf for a RAFT miniemulsion polymerization was synthesized and called DexN3-CTA , where and correspond to the number of N3-end alkyl chains (N3) and of dithiobenzoate CTA groups per 100 glucopyranosic units, respectively (Scheme 2a). On the one hand, N3-end alkyl chains have been chosen as hydrophobic groups due to their efficiency to hydrophobize dextran, leading to amphiphilic DexN3-dextran derivatives exhibiting surfactant properties (see Supporting Information). These derivatives have been successfully used to produce dextran-covered NPs via emulsion/evaporation [START_REF] Laville | Polysaccharide-covered nanoparticles with improved shell stability using clickchemistry strategies[END_REF][START_REF] Poltorak | Interfacial click chemistry for improving both dextran shell density and stability of biocompatible nanocapsules[END_REF] or nanoprecipitation [START_REF] Laville | Polysaccharide-covered nanoparticles with improved shell stability using clickchemistry strategies[END_REF] processes. In addition, azide functionality of such DexN3-is expected to be suitable for potential post-modification of final NPs surface by click chemistry. of both Z and R moieties clearly appeared (Figure 1b), thus ensuring its reactivity as RAFT agent. Modification degree of CTA groups ( ) could be tuned from 2 to 8% according to the experimental conditions. Those results were in quite good agreement with those previously obtained from native dextran [START_REF] Duong | Functionalizing Biodegradable Dextran Scaffolds Using Living Radical Polymerization: New Versatile Nanoparticles for the Delivery of Therapeutic Molecules[END_REF].

To be used as transurfs, the designed DexN3-CTA were expected to exhibit both surfactant and transfer agent properties. To check their surface activity, steady state surface tension measurements were performed with different series of DexN3-and DexN3-CTA (Figure S1). DexN3-(9 < <27) and DexN3-20CTA transurfs ( =20 and =3.7 or 7.5) were able to adsorb at the air/water interface and to reduce the surface tension of aqueous solutions. In the case of transurfs, the contribution of CTA groups to the decrease of surface tension seems less than that of N3-end alkyl groups, at least in the range of CTA modification degree tested here, i. e. below 8%. In fact, similar curves have been observed in case of DexN3-24 ( =24), DexN3- Ramirez., Babin, Durand, Six, & Nouvel, 2015 ), these results could be ascribed to the presence of thiocarbonylthio and cyano functions in CTA groups in the middle of the chain, that make them less prone to segregate towards oil phase, with respect to N3-end alkyl chains.

Nevertheless, we can expect that the hydrophobic character of those CTA groups (logP∼3.4) is high enough to allow direct contact of dithiobenzoate groups with the oil phase (log P ranging between 1.8 and 2.4 for initial droplet phase with M810/MMA ratio ranging from 10 to 50 vol.%), thus enabling their role as transurfs.

Miniemulsion polymerization using dextran-based transurf

After checking both the stability of the MMA miniemulsion containing M810 (a pharmaceutically acceptable triglyceride oil [START_REF] Hippalgaonkar | Injectable Lipid Emulsions-Advancements, Opportunities and Challenges[END_REF]))/DexN3-as co-stabilizer/stabilizer system under polymerization process, and the control of the MMA RAFT polymerization in miniemulsion using model conditions (molecular CTA + no-reactive DexN3-stabilizer) (see Supporting Information), optimized conditions were applied to DexN3-CTA transurfs. Our main challenge was to evaluate the potential of the transurf to act both as oil/water interface stabilizer and macro-CTA to generate DexN3--g-$ % & at the organic interface, in order to produce dextran-covered NCs with PMMA shell and M810 oily core. Thus, we first verified both the availability of CTA groups at the interface and their effective participation in RAFT polymerization.

Secondly, we evaluated the effects of M810 content and transurf structure on the polymerization kinetics and control. Initial molar ratio in the organic phase, estimated with the real amount of DexN3-τCTAγ at the interface evaluated in (a), and supposing that all the CTA groups were accessible for polymerization.

c Average nano-object diameter. Values under brackets correspond to Span (width of the distribution) calculated using 789$ : 0.9 -: 0.1 / : 0.5 . D(0.1), D(0.5) and D(0.9)

were the particle diameters at 10%, 50% and 90% of the particle volume size distribution.

d Average number of PMMA grafts per 100 glucopyranosic units estimated from 1 H NMR spectrum (Figure 1c) using n [ 4A @ A B A /5A CD M FGH IGJ /162 ]/X . A @ A B A and A CD are the areas under peaks (A'B') and (OH 1 , OH 2 , OH 3 and H α ), respectively. M FGH IGJ is the M of native dextran, 162 the molecular weight of one glucopyranosic unit and X is the average polymerization degree of PMMA grafts.

e Average CTA groups efficiency for transurfs estimated using Eff HO@ n/γ 100, where n and γ are the number of grafts and CTA groups per 100 glucopyranosic units, respectively.

f Weight fraction of PMMA homopolymers (non-attached to dextran) with respect to the total synthesized PMMA using

P QRSR T1 -T U VWX / YVWX $ M FGH Z[\]^_ `/
U %%X a ` 100, with U VWX the mass amount of DexN3-τCTAγ transurf at NCs surface, YVWX the molecular weight of one glucopyranosic unit of DexN3-τCTAγ, n the average number of PMMA grafts per 100 glucopyranosic units evaluated in (d), M FGH Z[\]^_ the M of PMMA grafts, U %%X the initial mass amount of monomer and a the monomer conversion. P QRSR was evaluated at two different conversions and average values are given.

Relative amount of transurfs at nanodroplets/NCs surface.

In the early stage of RAFT polymerization, DexN3-CTA transurfs were located at the monomer/water interface because of their surfactant properties (Figure S1) and mediated RAFT polymerization from their multiple reactive sites. As CTA groups were attached to dextran molecules via their R moieties, re-initiating radicals (R • ) were situated on the dextran backbone after the first addition-fragmentation step (Scheme 2b). Therefore, PMMA chains grew directly from the polysaccharide, via the R-group approach, to produce DexN3--g-$ % b at the oil/water interface that will constitute the NCs surface/polymeric shell at the end.

For Runs 1-4 (Table 1), [MMA]o/[CTA]o molar ratio (X) was estimated by taking into account the total amount of monomer in the system and the quantity of DexN3-CTA adsorbed at nanodroplets surface. This last quantity was considered in first approximation to be similar to the one at the surface of the final NCs, and was indirectly determined after NCs washing by dosage of the DexN3-CTA remaining in aqueous supernatant. In all cases, more than 90% of initial transurf was found to be located at the interface (Table 1). In contrast, similar analysis of PMMA latexes obtained with the model system (see Supporting Information) showed that only 60% of DexN3-20 was present in final NCs. This result could be surprising as polymerization conditions and specially [DexN3-]/[organic phase] weight ratio were chosen to avoid the presence of stabilizer into the aqueous phase, so as to prevent micellar or homogeneous nucleation. Nevertheless, in the model system, DexN3-20 desorption was more prone to occur under polymerization procedure or during particle washings as the stabilizer was only physically adsorbed onto NCs surface, whereas covalent linkage between dextran backbone and PMMA chains was expected to be formed in the case of transurfs, from the first moments of the polymerization. Transurf derivatives should thus be immobilized at NCs surface via their CTA groups, which would limit their desorption and explain their quantitative presence in final NCs.

Kinetics studies.

Figure 2 shows the first-order kinetic plots for RAFT polymerization in miniemulsion of 1).

In such conditions, AIBN initial mass remained constant while organic phase global volume increased with the amount of M810. Polymerization rate was thus expected to slow down when increasing M810/MMA volume ratio as a result of the reduction of AIBN concentration inside nanodroplets. Nevertheless, as observed in stability studies, the increase of M810 content from 10 to 50% vol.% (which corresponded to initial organic phase volumes of 1.1 mL and 1.65 mL, respectively) resulted only in a slight increment of initial nanodroplets average size (from 102 to 117 nm) (see Supporting Information). As a consequence, the number of nanodroplets considerably increased from one experiment to another, which led to faster polymerization kinetics and, hence, offset the effect of AIBN concentration decrease, resulting in similar kinetics.

As for the model system (see Supporting Information

DexN3--g-cdee. e c analysis.

Attempting to confirm the covalent linkage between PMMA shell and dextran coverage of NCs, DexN3--g-$ % b glycopolymers produced at the oil/water interface were purified from M810 and from free PMMA homopolymers (not attached to dextran), by several washings of dried NCs with THF. These glycopolymers were also characterized with their weight fraction of PMMA (FPMMA) determined by equation 3, where -fg is the molecular weight of one glucopyranosic unit of DexN3-τCTAγ.

P $ hhhh $ $ hhhh $ + 100 -fg 3
For copolymers produced in Runs 1 -4, n was estimated from 1 H NMR spectra in DMSO-d6 (Table 1). 1 H NMR spectrum of DexN3-20-g-1.8PMMA7800 elaborated from DexN3-20CTA3.7 (Run 3) is given in Figure 1c as example. Typical signals of dextran and PMMA parts are clearly observed, especially methyl (B', 0.5-1.0 ppm), methylene (A', 1.5-2.0 ppm) and O-CH3 proton peaks (C', 3.6 ppm) attributed to the repeating unit of PMMA grafts, and hydroxyl and anomeric proton peaks (4.1-5.4 ppm) from the dextran backbone. Unfortunately, ester linkages between the two parts could not be proven by this method. DexN3--g-$ % b were therefore studied by 2D Diffusion-Ordered Spectroscopy (DOSY) 1 H NMR (Figure 3). This technique allowed separation of the NMR signals of different species according to their diffusion coefficient. It has previously been used to discriminate between a grafted copolymer and the corresponding homopolymer mixture [START_REF] Soliman | Amphiphilic photosensitive dextran-g-poly(o-nitrobenzyl acrylate) glycopolymers[END_REF]. On the one hand, the 2D DOSY 1 H NMR spectrum of DexN3-20g-1.8PMMA7800 was recorded in DMSO-d6 (Figure 3a). As shown, a single self-diffusion coefficient was observed for all the protons from both dextran and PMMA parts (D = 4.47× 10 -10 m 2 s -1 ), which suggested that PMMA grew effectively from CTA groups on dextran. On the other hand, a mixture (same weight composition as for the copolymer DexN3-20-g-1.8PMMA7800) of the precursor DexN3-20CTA3.7 transurf and a PMMA homopolymer having roughly the same average molecular weight of PMMA grafts was also analyzed (Figure 3b).

In this last case, 2D DOSY spectrum provided two different diffusion coefficients (D = 3.16 × 10 -11 m 2 s -1 and D = 1.78 × 10 -10 m 2 s -1 ) for transurf and PMMA, respectively. The presence of these two diffusion coefficients, compared to only one (at a different value) in case of DexN3-20-g-1.8PMMA7800, proved that PMMA grafts were really covalently linked to dextran backbone, resulting in a DexN3--g-$ % b glycopolymer.

Figure 3. 2D DOSY 1 H NMR spectra of a) DexN3-20-g-1.8PMMA7800 (FPMMA= 43%) obtained from Run 3 (Table 1) at 12% of conversion and b) mixture of PMMA7100 and DexN3-20CTA3.7 (43/57; w/w).

Finally, we wanted to characterize those DexN3--g-$ % b glycopolymers by SEC-MALLS. Nevertheless, it was difficult to find an appropriate solvent able to well solubilize both the hydrophilic polysaccharide and the hydrophobic PMMA parts. Despite solubility problems resulting in the appearance of numerous aggregate peaks on the SEC trace, chromatograms of purified DexN3--g-$ % b (i.e. after washing with THF-Figure S6)

clearly showed a shift of the molecular weight distribution toward higher molar masses in comparison with the chromatogram of the precursor transurf, which further attested to the copolymer formation. Nonetheless, accurate average molar masses were not accessible from these SEC-data due to the above-mentioned solubility issues. Non-purified DexN3--g-$ % b (i.e. before THF washings) were also investigated. In comparison with chromatograms of purified glycopolymers, an additional smaller peak evolving with conversion was detected at high elution time. This peak, disappearing after purification, was found to correspond to PMMA homopolymers (non-attached to dextran) formed during polymerization, as confirmed by 1 H NMR spectrum of the product extracted with THF. This observation was not a surprise. The production of a small percentage of homopolymer is inherent to the RAFT process since chains are initiated by AIBN decomposition. Thus, in addition to PMMA chains re-initiated by CTA groups and growing from the dextran backbone at the oil/water interface, there is also a small fraction of PMMA chains coming from AIBN and propagating within the organic phase. Furthermore, irreversible transfer reactions could also eventually lead to homopolymer formation. For all experiments, homopolymer fraction (P ijUj ) was evaluated to about 20 wt% of the total produced polymer amount (Table 1), which remains quite reasonable and below the maximum amount evaluated for a

[CTA]0/[AIBN]0 ratio of 3. We can expect that this relatively low fraction would not have a significant adverse impact on the desired core-shell morphology control.

Polymerization control and CTA groups efficiency.

In order to ascertain the degree of RAFT polymerization control, PMMA grafts were deliberately uncoupled from dextran backbone, then characterized by SEC-MALLS. Total PMMA recovery was achieved under basic conditions already proven to be harmless for PMMA grafts [START_REF] Dupayage | PMMAgrafted dextran glycopolymers by atom transfer radical polymerization[END_REF][START_REF] Ramirez | Multi-reactive surfactant and miniemulsion Atom Transfer Radical Polymerization: An elegant controlled one-step way to obtain dextran-covered nanocapsules[END_REF]. SEC of uncoupled PMMA chains exhibited monomodal distributions at low conversion and a clear shift toward higher molar masses with conversion (Figure 4a). For conversions above 50%, a small molecular weight shoulder was however observed suggesting a small proportion of irreversible deactivation by bimolecular termination between two PMMA grafts, or more probably between a PMMA graft and a PMMA homopolymer. When comparing polymerizations carried out with the same transurf but different M810 contents, similar SEC traces were observed at analogous conversions indicating that M810 amount has no influence on RAFT polymerization control. Furthermore, molar mass distributions of PMMA homopolymers (unlinked to dextran) overlaid pretty well with those of PMMA grafts obtained at the same conversion (Figure S7). This showed that the exchange of thiocarbonylthio groups between grafted and free PMMA chains was quite effective to allow the control of macromolecular parameters of both types of chains. Overall these results indicated the absence of noticeable transfer or termination reactions, except a small proportion of termination by recombination of PMMA grafts (no shoulder was detected in case of homopolymers). Bimolecular termination between a PMMA graft and a PMMA homopolymer was more prone to occur at high conversion and with consequent amount of M810 in the organic phase. Actually, sufficient amount of M810 in the organic phase was expected to favor phase segregation between the oily core and the polymer shell (see 3.3), and thus, the geographic proximity between free PMMA chains (growing into the organic phase)

and PMMA grafts (growing at the interface). Bimolecular termination between two PMMA grafts was less probable to happen. Furthermore, such termination would have resulted in the reticulation of the system, which was never observed in any case.

Theoretical Mn

Run 1, 10 vol.% (♦) Run 2, 25 vol.% (▲) Run 3, 50 vol.%. See Table 1 for other conditions. Theoretical ' (dotted lines) was evaluated using ' 100 a k where x and 100 are the monomer conversion and the molecular weight of a PMMA unit, respectively. Curve for X = 393 is given.

The evolution of experimental $ of PMMA grafts with conversion for Runs 1-3 is shown as a function of theoretical $ in Figure 4b. In all cases, experimental $ evolved linearly with conversion until 80% of conversion without appearance of noticeable transfer or termination reactions. In addition, Ð remained considerably below 1.2. All these results further attested of RAFT control during almost the whole polymerization. Experimental hhhh $ were however much higher than the theoretical ones (calculated with the adjusted average value of X =

[MMA]o/[CTA]o=393) indicating that not all CTA groups participated in the polymerization (Figure S8 for additional results of Run 4, X = 402). The comparison between the number of grafts (n) estimated from 1 H NMR spectra and the number of CTA groups along dextran backbone ( ) allowed us to evaluate an average efficiency of CTA groups (Eff HO@ ) of about 48% (Table 1). Roughly half of the initial CTA groups of DexN3-CTA transurfs located at the interface, effectively resulted in a PMMA grafted chain. Similar lower efficiencies have been already observed for other polysaccharides bearing reactive groups when used for controlling ATRP [START_REF] Dupayage | PMMAgrafted dextran glycopolymers by atom transfer radical polymerization[END_REF][START_REF] Ferji | Polymersomes from Amphiphilic Glycopolymers Containing Polymeric Liquid Crystal Grafts[END_REF] in homogeneous media. One possible cause seemed to be the presence of intramolecular termination reactions at the very beginning of the polymerization resulting in the loss of RAFT re-initiating radicals (R • ). In our case, the reaction takes place in a heterogeneous environment. So, the transurf conformation at the oil/water interface is more likely the key factor limiting the availability of some CTA groups for polymerization if they are not facing to the organic phase, which was the main challenge of this work. Finally, CTA group efficiency appeared to be the same for both DexN3-20CTA3.7 and DexN3-20CTA7.5, and remained unchanged whatever the M810/MMA volume ratio in agreement with our previous results for miniemulsion ATRP of the microscope electron beam since the polymeric shell was less sensitive to irradiation damage (Figure S10). These observations provided direct evidence of core-shell structure formation. Improved studies will be however needed to further characterize NCs morphology.

Nano-objects cytocompatibility

Formulated NCs are constituted of an oily liquid biocompatible M810 core, an inner shell of PMMA (frequently used in implantable medical devices [START_REF] Frazer | PMMA: An Essential Material in Medicine and Dentistry[END_REF]) and an outer shell of dextran (well-known biodegradable and bioeliminable polysaccharide [START_REF] Posocco | Polysaccharides for the Delivery of Antitumor Drugs[END_REF]). In order to check the potential of these NCs for intravenous drug administration, preliminary cytocompatibility studies on vascular smooth muscle cells were performed in vitro. NCs prepared with the model system (see Supporting Information), called MOD, and with transurfs (called CTA-PMMA) were both analyzed.

Metabolic activity of vascular cells was measured by monitoring the conversion of MTT to formazan. The reduction of MTT is catalyzed by mitochondrial dehydrogenase enzymes and is therefore a measure for cell viability. After 24 hours, results expressed as percentages did not show any variation whatever the concentration or NCs type, when compared to the control condition (no NC) (Figure 6). The MOD and CTA-PMMA NCs appeared to be cytocompatible with vascular smooth muscle cells. 1) towards rat vascular smooth muscle cells (A-10) after 24 h incubation at 37°C. 100% of metabolic activity (MTT assay) represents control cells incubated with PBS.

Results expressed as mean ± standard error of the mean, n = 3.

Conclusions

As stated, we designed dextran-based transurfs able to produce oily-core/PMMA shell NCs by RAFT interfacial miniemulsion polymerization. The two major challenges of this work were to introduce CTA functionalities onto dextran in order to synthesize a multi-reactive transurf (acting both as macro-CTA and stabilizer) and to check its ability to confine RAFT miniemulsion polymerization of MMA at the oil/water interface. About a half of the CTA groups along dextran backbone were found to effectively initiate a PMMA grafted chain.

Figure 1

 1 Figure 1. 1 H NMR spectra (DMSO-d6) of a) DexN3-20, b) DexN3-20CTA3.7 and c) DexN3-20-g-

1H

  NMR and 2D DOSY 1 H NMR spectra were recorded on a Bruker Avance 300 apparatus (30,013 MHz, 25 •C) in DMSO-d6. 1024 Scans were recorded. Droplet and NCs sizes were measured by using a Laser Diffraction Particle Size Analyzer (Mastersizer 2000 Malvern Instruments). Washed NCs suspension (8 wt% solid content) was diluted by a factor of 200 and NCs morphology was observed by cryo-Transmission Electron

Scheme 2 .

 2 Scheme 2. a) Synthesis of DexN3-CTA transurfs. b) RAFT polymerization of MMA from DexN3-CTA via the R-group approach.

  20CTA3.7 (global modification degree of + ~24) and DexN3-20CTA7.5( + ~27), whereas a bigger decrease in surface tension was observed for DexN3-27 ( =27). Even if CTA groups have global hydrophobic character (log P∼3.4 as calculated by group contribution methods,

  MMA using DexN3-CTA transurfs. A linear relationship between ln([M]o/[M]t) and polymerization time was observed until at least 70% conversion, whatever the transurf or the M810 content. In addition, similar polymerization kinetics with reproducible delay period were observed when increasing M810 amount from 10 vol.% to 50 vol.% compared to MMA, while keeping [MMA]0/[CTA]0 constant (Runs 1-3). This result was quite surprising as these experiments were carried out with the same transurf, [CTA]o/[AIBN]o ratio (equal to 3), and MMA volume.

Figure 2 .

 2 Figure 2. Ln([M]o/[M]t) versus time. RAFT polymerization of MMA in miniemulsion at 80°C using DexN3-CTA transurfs (or DexN3-20 stabilizer). (*) Run 0, DexN3-20, [CTA]o = 0, 10 vol.% M810 (•) Run 1, DexN3-20CTA3.7, X = 393, 10 vol.% M810 (♦) Run 2, DexN3-20CTA3.7, X = 393, 25 vol.% M810 (▲) Run 3, DexN3-20CTA3.7, X = 402, 50 vol.% M810 ( ) Run 4, DexN3-20CTA7.5, X = 204, 25 vol.% M810 (see Table1).

  ), both studied DexN3-CTA transurfs appeared to slow down the miniemulsion polymerization of MMA. Indeed, DexN3-20CTA3.7 ([AIBN]o = 5.7 mM, Run 2) and DexN3-20CTA7.5 ([AIBN]o = 11.9 mM, Run 4) showed much slower kinetics when compared to a conventional radical polymerization system ([AIBN]o = 6.7 mM, Run 0). This slow down effect suggested both the availability of CTA groups at the oil/water interface and their effective involvement in growth of PMMA chains. As expected, DexN3-20CTA7.5 (Run 4) gave faster polymerization rate than DexN3-20CTA3.7 (Run 2). Since DexN3-20CTA7.5 was bearing more CTA groups, AIBN concentration was almost doubled in Run 4 with respect to Run 2 to keep constant the [CTA]o/[AIBN]o ratio. Furthermore, no delay period was observed with DexN3-20CTA7.5 once again probably because of the higher initiator amount used in this experiment.

Figure 4 .

 4 Figure 4. Evolution of a) SEC traces (Refractive Index detector) of PMMA grafts (Run 2) and b) experimental M ' (full symbols), Dispersity Ð (open symbols) versus conversion. Conversions are given in % on figure a). RAFT polymerization of MMA in miniemulsion at 80°C using DexN3-20CTA3.7 transurf and various amounts of M810 in the organic phase (•)

Figure 5 .

 5 Figure 5. Assembly of Cryo-TEM micrographs of final NCs obtained from Run 2. The black

Figure 6 .

 6 Figure 6. Cytocompatibility of MOD (prepared with a [MMA]o/[CPDB]o molar ratio of 700 and 25 vol.% of M810 compared to MMA, see Supporting Information) or CTA-PMMA NCs (Run 2, Table1) towards rat vascular smooth muscle cells (A-10) after 24 h incubation at 37°C. 100% of metabolic activity (MTT assay) represents control cells incubated with PBS. Results expressed as mean ± standard error of the mean, n = 3.

Table 1

 1

summarizes all experimental recipes used in the current study, as well as the average size of initial nanodroplets and final NCs. In any case, latexes were very stable during polymerization procedure. Distribution size of the final NCs were roughly similar to the one of the initial nanodroplets, in agreement with preliminary stability assays performed with DexN3-20 (see Supporting Information). Depending on experimental conditions, and especially on M810 volume ratio, final solid content varied from 8 to 13 wt% in water.

Table 1 .

 1 Miniemulsion polymerization of MMA at 80°C using DexN3-CTA transurf or DexN3-20 stabilizer with 1.1 mL of MMA. [DexN3-CTA (or DexN3-)] = 10 g/L and [CTA]0/[AIBN]0 = 3.

	Run (DexN3-CTA or DexN3-)/	[AIBN]o M810/MMA (vol.%)	Stabilizer or Transurf	DexN3-CTA adsorbed	[MMA]o/[CTA]o (or X) (b)	Nano-objects diameter (nm) (c)	Grafts number	*++ ,-. (%) (e)	/ 0121 (f)
		organic phase				(%) (a)				(n) (d)
		(wt%)						After	Final
								degassing
	0	13.2	6.7	10	DexN3-20	-	-	113	110	-	-	-
								(1.30)	(1.10)
	1	13.2	6.7	10	DexN3-20CTA3.7	94	393	102	102	1.8±0.3	48	20
								(1.00)	(0.83)
	2	11.6	5.7	25	DexN3-20CTA3.7	94	393	112	109	1.7±0.3	45	25
								(1.49)	(1.30)
	3	9.7	3.5	50	DexN3-20CTA3.7	92	402	117	119	1.8±0.3	48	25
								(1.37)	(1.14)
	4	11.6	11.9	25	DexN3-20CTA7.5	94	204	105	110	3.5±0.3	47	17
								(1.31)	(1.30)

a Relative molar amount in NCs. Expressed as function of the initially introduced DexN3-τCTAγ. b

ACKNOWLEDGEMENTS

C. Nouvel and L.M Forero Ramirez acknowledge support from ANR JCJC ANR-12-JS08-0003-01 NANOCAPDEX for funding and PhD Research Fellowship, respectively.

The authors express their highest gratitude to Olivier Fabre for NMR analyzes, to Marie-Christine Grassiot for help in SEC measurements andto Isabelle Fries for cytotoxicity assays.

MMA using dextran-based inisurfs [START_REF] Ramirez | Multi-reactive surfactant and miniemulsion Atom Transfer Radical Polymerization: An elegant controlled one-step way to obtain dextran-covered nanocapsules[END_REF]. A steric hindrance effect in the vicinity of CTA groups restricting the access to C=S function does not seem to be present in the range of studied CTA modification degrees.

Nano-objects morphology

Indirect confirmation of an oily-core/polymeric shell morphology of final objects was provided by MDSC analysis. The obtained thermograms (Figure S9) showed that NCs made with 25-50 vol.% of M810 (Runs 2, 3 and 4) were effectively two-phase systems having: i) a plasticized amorphous phase of PMMA/M810 (11 / 89 w / w, Tg = 98 °C) and ii) a pure M810 liquid phase exhibiting one melting transition (Tm = -4°C). On the contrary, nano-objects formulated with 10 vol.% of M810 (Run 1) displayed only a single glass transition event indicating a total miscibility of two components. These results were in quite agreement with our previous studies on PMMA/M810 blends miscibility as M810 was shown to plasticize PMMA until a weight fraction of 11 wt% [START_REF] Ramirez | Multi-reactive surfactant and miniemulsion Atom Transfer Radical Polymerization: An elegant controlled one-step way to obtain dextran-covered nanocapsules[END_REF].

In order to prove NCs morphology in a direct way, final nano-objects were analyzed by Cryogenic-Transmission Electron Microscopy (cryo-TEM). Electron micrograph of NCs obtained with 25 vol.% of M810 in the organic phase (Run 2, Table 1) at 93% of conversion is shown in Figure 5. Cryo-TEM image showed the sphericity of synthesized objects as well as the average diameter determined by Laser granulometry, which varies from around 200 nm to 50 nm. A few particles are even smaller in that case the inner oily core is not clearly seen.

The lack of sufficient contrast between plasticized PMMA and pure M810 phases render the visualization of the oily-core/polymeric shell structure under low dose conditions not simple.

The core shell structure is best seen on small objects. On the larger objects the PMMA layer is just slightly darker than the oily core. The shell thickness is around 25 nm on all objects of run 2, Table 1. Internal liquid oil cavity was more visible for large objects after exposure to About 80 wt% of the total produced PMMA was effectively attached to dextran backbone. In any case, polymerization was controlled until high conversion as concluded from the analysis of uncoupled PMMA grafts deliberately removed from DexN3--g-$ % b . Phase segregation between PMMA shell and M810 core was evidenced.

Overall these results highlight the value of our novel dextran-based transurf to produce dextran-covered oily-core NCs having different oil contents. Such NCs can be potentially used in drug delivery applications as indicated by preliminary in vitro cytotoxicity tests.

Complementary biological tests, deep characterization of covalently linked dextran coverage, as well as post-functionalization of final NCs via the azide functions will be reported soon.

The possibility of extending this method to RAFT copolymerization of MMA with a pHresponsive monomer will be also studied in the near future.


Reda Mustapha

Abdelhamid Senouci

Senior Member, IEEE Mellouk

A robust uncertainty-aware cluster-based deployment approach for WSNs: coverage, connectivity, and lifespan

Keywords: Belief Functions Theory, Wireless Sensor Networks, Clustering, Fusion, Deployment, Coverage, Connectivity, Detection, Surveillance Applications, False Alarm. I. INTRODUCTION

Predicting the expected performance of Wireless Sensor Networks (WSNs) is the key to their successful deployment. This paper investigates the following fundamental problem: how to judiciously plan the physical and the logical topologies of a WSN so that performance demands including network connectivity, sensing coverage quality, reliability, and lifetime are all satisfied with the least possible cost. To handle the uncertainty related to sensor connectivity and coverage, we devise a probabilistic-based communication cost model, and we exploit the belief functions theory to define a generic evidence fusion scheme that captures several characteristics of real-world applications. The uncertainty-aware cluster-based WSNs deployment problem is formulated as a multi-objective binary nonlinear and non-convex optimization problem, and an efficient heuristic using genetic algorithms is investigated.

Using both simulations and testbed-based experiments, we show that the proposed deployment approach can fulfill the user performance needs, which confirms that the deployment of real-world fusion-based WSNs with predictable performance is possible.

improvement could be expected with this approach, as the logical topology is mainly constrained by the physical topology of the network. Moreover, only a few metrics could be impacted by this approach. For instance, modifying the logical topology has little to no impact on coverage as the latter is more related to the sensors' positions.

As explained previously, many optimizations can be performed to enhance the performance of WSNs. Still, we consider that the most significant optimizations are those accomplished at the pre-deployment step to build the best possible topology that meets explicit performance requirements. In fact, the types, numbers, and locations of sensors have to be duly planned in order that performance requirements in terms of coverage, connectivity, and lifespan are all met while keeping the cost affordable. In the literature, this kind of deployment practice is referred to as deterministic WSNs deployment. There has been much related research on the deterministic deployment of WSNs in security monitoring [START_REF] Fanti | An integrated framework for binary sensor placement and inhabitants location tracking[END_REF], [START_REF] Cao | 3d terrain multiobjective deployment optimization of heterogeneous directional sensor networks in security monitoring[END_REF], [START_REF] Thomas | Energy-efficient military surveillance: Coverage meets connectivity[END_REF]. These previous works are mainly based on a flat architecture. They focus solely on the coverage rate (characterized by the detection probability) and do not consider the quality of coverage (i.e., they ignore false alarms).

Recently, Tan et al. [START_REF] Tan | Exploiting data fusion to improve the coverage of wireless sensor networks[END_REF] showed that the quality of coverage is greatly enhanced by data fusion when utilizing the collaboration among sensors. This has incited the development of new proposals [START_REF] Ababnah | Optimal sensor deployment for value-fusion based detection[END_REF], [START_REF] Ababnah | Lqr formulation of sensor deployment for decision fusion based detection[END_REF], [START_REF] Chang | Sensor placement algorithms for fusion-based surveillance networks[END_REF], [START_REF] Senouci | Fusion-based surveillance wsn deployment using dempster-shafer theory[END_REF] that adopt data fusion techniques. These proposals consider tiered architecture and use different tools such as optimal control theory [START_REF] Ababnah | Optimal sensor deployment for value-fusion based detection[END_REF], [START_REF] Ababnah | Lqr formulation of sensor deployment for decision fusion based detection[END_REF], probability theory [START_REF] Chang | Sensor placement algorithms for fusion-based surveillance networks[END_REF], [START_REF] Yang | Graphical deployment strategies in radar sensor networks (rsn) for target detection[END_REF], fuzzy theory [START_REF] Collotta | A fuzzy data fusion solution to enhance the QoS and the energy consumption in wireless sensor networks[END_REF], and Dempster-Shafer evidence theory [START_REF] Senouci | Fusion-based surveillance wsn deployment using dempster-shafer theory[END_REF]. Most of these approaches enhance the performance of the WSN by taking advantage of the collaboration between sensors.

Nevertheless, these approaches do not take into account several deployment-related issues such as connectivity and network lifespan. Furthermore, most of them do not specify how and where the data fusion process should be handled, and how sensor data should be communicated to the fusion center. Therefore, practical situations are not handled by this type of research. Moreover, other approaches [START_REF] Yang | Graphical deployment strategies in radar sensor networks (rsn) for target detection[END_REF], [START_REF] Collotta | A fuzzy data fusion solution to enhance the QoS and the energy consumption in wireless sensor networks[END_REF] consider the base station as the fusion center. It is evident that this latter solution is not sustainable and could exhibit scalability issues.

In this work, we are attempting to bridge this gap by exploring simultaneously a cluster-based WSN architecture and an efficient Dempster-Shafer based fusion scheme while considering a full set of deployment-related issues, which is more suitable for surveillance applications. To the best of our knowledge, this paper is the first to comprehensively addresses the problem of fusion-based deterministic WSNs deployment by jointly considering sensing coverage quality, network connectivity, lifetime, reliability, and deployment cost. Consequently, the WSNs deployment issue becomes more complex but has more practical significance. The key contributions of this work are as follows.

1) The problem at hand is formulated as a nonlinear optimization problem with binary variables. Various aspects of real-life applications including uncertain sensor measurements, sensor's spatial distribution, unreliable connectivity, sensor reliability, and harsh deployment environments are captured in this framework.

2) As the formalized problem is NP-hard, an efficient heuristic is developed to solve it.

3) Using both simulations and testbed-based experiments, we show that the proposed deployment approach can fulfill the user performance needs.

The rest of this paper is structured as follows. Section II reviews related work. Section III summarizes the key concepts of the evidence fusion model and presents our communication cost prediction approach. The uncertaintyaware cluster-based WSNs deployment problem is formalized in Section IV, and resolved in Section V. The evaluation of our proposed approach via simulations and experiments is presented in Section VI. Finally, Section VII draws the main conclusions of this paper.

II. RELATED WORK

The problem of cluster-based WSNs deployment could be approached in two different ways (levels), namely: at the logical topology or rather at the physical topology. In this section, previous works related to both approaches are discussed.

A. Clustering approaches

Clustering approaches [START_REF] Abbasi | A survey on clustering algorithms for wireless sensor networks[END_REF], [START_REF] Fanian | Cluster-based routing protocols in wireless sensor networks: A survey based on methodology[END_REF] target the logical topology of the network. More precisely, they target the routing layer. The main idea of these approaches is to group the sensors into clusters to achieve network scalability.

Additionally, clustering has numerous advantages. It can conserve communication bandwidth, and reduce energy dissipation by using fusion schemes to minimize the number of messages forwarded to the sink. However, clustering approaches care mostly about network connectivity and route stability, without much concern about critical design goals of WSNs such as coverage [START_REF] Abbasi | A survey on clustering algorithms for wireless sensor networks[END_REF], [START_REF] Ghosal | Lifetime optimizing clustering structure using archimedes' spiral-based deployment in wsns[END_REF]. For these reasons, in the remainder of this paper, we will not discuss such approaches.

B. Deterministic sensor placement approaches

We refer to deterministic deployment strategies that exploit the clustering principle as cluster-based deterministic deployment strategies. There has been little research in this area. Previous deployment approaches have adopted simplistic combination techniques such as averaging. Recently, Xing et al. [START_REF] Xing | Data fusion improves the coverage of wireless sensor networks[END_REF] showed by means of probability theory that value fusion enhances the coverage of WSNs.

Chang et al. [START_REF] Chang | Sensor placement algorithms for fusion-based surveillance networks[END_REF] considered both detection probabilities and false alarm rates under a value fusion scheme [START_REF] Tan | Exploiting data fusion to improve the coverage of wireless sensor networks[END_REF], and formulated the WSNs deployment problem as a nonlinear and non-convex optimization problem. To solve this latter problem, they suggested the application of the constrained simulated annealing, which is a discrete global minimization algorithm of a high computational complexity. This limits their approach to rather small networks. To overcome this limitation, they devised a relatively low computational complexity heuristic. Simulation results were provided for the validation of the proposed method. Using the above-mentioned value fusion approach [START_REF] Tan | Exploiting data fusion to improve the coverage of wireless sensor networks[END_REF], Zhang et al. [START_REF] Zhang | Cost-efficient barrier coverage with a hybrid sensor network under practical constraints[END_REF] presented a scheme to achieve barrier coverage in a hybrid wireless sensor network. The worst-case complexity of the proposed scheme is O(n 4 ) where n is the number of sensors.

Ababnah et al. [START_REF] Ababnah | Sensor deployment in detection networks -a control theoretic approach[END_REF] used the optimal control theory to formulate the deterministic deployment of WSNs as an optimal control problem, with the sensors' positions acting as control variables. In [START_REF] Ababnah | Optimal sensor deployment for value-fusion based detection[END_REF], this nonlinear optimal control problem was linearized and solved under several approximations while considering a value fusion scheme. The time complexity of the devised solution is O(3n 6 + 4n 4 ). In another recent work, a similar algorithm was introduced by Ababnah et al. [START_REF] Ababnah | Lqr formulation of sensor deployment for decision fusion based detection[END_REF] where the decision fusion rule was implemented via the majority rule. The time complexity of the suggested algorithm is O(3n 6 + 4n 4 ). It is worth noting that previous works [START_REF] Ababnah | Optimal sensor deployment for value-fusion based detection[END_REF], [START_REF] Ababnah | Lqr formulation of sensor deployment for decision fusion based detection[END_REF], [START_REF] Chang | Sensor placement algorithms for fusion-based surveillance networks[END_REF] rely on simplistic fusion approaches, and disregard completely several issues and challenges involved in the design of WSNs such as harsh deployment environments and sensor reliability. Very recently, in [START_REF] Senouci | Fusion-based surveillance wsn deployment using dempster-shafer theory[END_REF], we have considered a radically different approach by exploiting the belief functions theory [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF] that allows taking into consideration not only the uncertainty in sensor data but also many aspects of real-life applications. More precisely, we have defined an evidence-based sensing mode where the sensor's output is modeled by a belief function rather than a Bayesian probability distribution. In addition, we have described the process of constructing belief functions from raw data returned by sensors [START_REF] Senouci | Fusion-based surveillance wsn deployment using dempster-shafer theory[END_REF]. This belief functions theory based fusion scheme has been exploited to devise a fusion-based deterministic deployment approach. Obtained results

showed that significant improvement could be achieved when exploiting evidence combination.

The major drawbacks of all above-discussed fusion-based deterministic deployment approaches [START_REF] Ababnah | Optimal sensor deployment for value-fusion based detection[END_REF], [START_REF] Ababnah | Lqr formulation of sensor deployment for decision fusion based detection[END_REF], [START_REF] Chang | Sensor placement algorithms for fusion-based surveillance networks[END_REF], [START_REF] Senouci | Fusion-based surveillance wsn deployment using dempster-shafer theory[END_REF] are:

• Although the generated topologies are hierarchical, the exact location of the cluster-heads is not determined.

Indeed, these approaches focus on generating clusters, where each cluster comprises one cluster-head. However, they do not explicitly designate the cluster-heads within the clusters.

• Although sensors are supposed to collaborate, these approaches completely ignore network connectivity.

• The network lifespan issue is not addressed.

In the present paper, we tackle all of the above-mentioned drawbacks while investigating different mathematical tools. First, to handle the uncertainty in sensor data (caused by measurement errors due to the hardware or the environment), we exploit a belief functions theory based fusion scheme. Second, to take into consideration both network connectivity and lifespan, we devise a probabilistic-based model that allows an accurate prediction of communication cost and network lifespan. The next section describes these models in more detail.

III. COVERAGE, CONNECTIVITY, AND LIFESPAN MODELS

In this section, we present the mathematical models considered in this work. First, we summarize the key concepts of the evidence-based sensing model that we have proposed very recently in [START_REF] Senouci | Fusion-based surveillance wsn deployment using dempster-shafer theory[END_REF]. Second, we present our probabilistic-based communication cost model.

A. Coverage model

Unlike prior efforts, we consider an evidence-based decision scheme. In this latter, sensor nodes do not generate binary decisions but produce belief functions instead. In this section, we detail our method for constructing and manipulating these belief functions also referred to as basic belief masses (bbm).

1) Evidence construction:

In surveillance applications, the main aim is to detect whether a target/event is present or not. The process of detection depends not only on the actual presence of the target/event but also on the RoI characteristics and the sensor's capabilities. Therefore, when a target/event is present in the RoI, the WSN will either correctly detect it or will miss it. From a modeling perspective, two states are necessary to express this fact:

θ 0 (target/event present and not detected) and θ 1 (target/event present and detected). Consequently, our Frame of Discernment (FoD) is the set Θ t = {θ 0 , θ 1 }.

The uncertain raw sensory data can be translated into basic belief masses as follows: for a sensor s i and relatively to a target/event at point p ∈ RoI, three inputs are defined: the mass assigned to no detection m Θ t d i/p (θ 0 ), the mass assigned to detection m Θ t d i/p (θ 1 ), and the unassigned mass m Θ t d i/p (θ 0 , θ 1 ). By definition, the summation of the three belief masses always equals one. Therefore, although three masses are considered, there are only two independent ones. For instance, we can choose m Θ t d i/p (θ 0 ) and m Θ t d i/p (θ 1 ). The mass m Θ t d i/p (θ 1 ) reflects the belief in a target/event presence at a location p, the bbm m Θ t d i/p (θ 0 ) represents the opposite, and the bbm m Θ t d i/p (θ 0 , θ 1 ) quantifies the sensor uncertainty.

Given a sensor s i that believes, with a degree of belief b d i/p , that there is a target/event located at p, the following mapping is used to compute the probability masses:

m Θ t d i/p (x) =                    (1 -u i ) • (1 -b d i/p ) if x = {θ 0 }, ( 1
-u i ) • b d i/p if x = {θ 1 }, u i if x = {θ 0 , θ 1 }, 0 if x = {∅}.
where u i ∈ [0, 1] is the uncertainty associated with the sensor s i decision.

As explained above, when a target/event is actually not present in the RoI, the WSN could report a false detection.

Such a decision is called a false alarm. From a modeling perspective, two states are necessary to express this fact:

θ 2 (target/event absent and not detected), θ 3 (target/event absent and detected). Therefore, the FoD is the set

Θ nt = {θ 2 , θ 3 }.
Assuming that a sensor s i has a false alarm rate b fi , its uncertain sensory data are translated into basic belief masses by defining a belief function m Θ nt f on Θ nt as follows:

m Θ nt fi (x) =                    (1 -u i ) • (1 -b fi ) if x = {θ 2 }, (1 -u i ) • b fi if x = {θ 3 }, u i if x = {θ 2 , θ 3 }, 0 if x = {∅}.
It should be noted here, that both formulations m Θ t d i/p and m Θ nt fi meet Appriou's axioms [START_REF] Appriou | Formulation et traitement de l'incertain en analyse multisenseurs[END_REF].

2) Decision combination: Decisions collected from multiple sensors are combined through the combination operation for final decision making. To combine distinct pieces of evidence on the same FoD, different combination rules could be used such as the Dempster-Shafer's rule of combination [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF], Yager's rule [START_REF] Yager | On the dempster-shafer framework and new combination rules[END_REF], and the Proportional Conflict Redistribution rules [START_REF] Smarandache | Advances and Applications of DSmT for Information Fusion (Collected Works)[END_REF]. In this work, we consider the Dempster-Shafer's rule of combination. For N sensors, the combination of the N belief functions m Θ t d1 , . . . , m Θ t dN using the Dempster-Shafer's rule of combination yields the following belief function m Θ t d :

m Θ t d (θ 0 ) = 1 -N i=1 (1 -m Θ t di (θ 0 )) • k d m Θ t d (θ 1 ) = 1 - N i=1 (1 -m Θ t di (θ 1 )) • k d m Θ t d (Θ t ) = N i=1 m Θ t di (Θ t ) • k d (1)
where

k d = 1 N i=1 (1 -m Θ t di (θ 0 )) + N i=1 (1 -m Θ t di (θ 1 )) -N i=1 m Θ t di (Θ t )
In the same way, the combination of the N belief functions m Θ nt f1 , . . . , m Θ nt fN using the Dempster-Shafer's rule of combination yields a bba m Θ nt f that has the following expression:

m Θ nt f (θ 2 ) = 1 -N i=1 (1 -m Θ nt fi (θ 2 )) • k f m Θ nt f (θ 3 ) = 1 - N i=1 (1 -m Θ nt fi (θ 3 )) • k f m Θ nt f (Θ nt ) = N i=1 m Θ nt fi (Θ nt ) • k f (2)
where

k f = 1 N i=1 (1 -m Θ nt fi (θ 2 )) + N i=1 (1 -m Θ nt fi (θ 3 )) - N i=1 m Θ nt fi (Θ nt )
3) Decision making: When decisions must be taken, the belief function undergoes a transformation called the pignistic transformation. This latter generates a probability distribution also known as the pignistic probability function. In this work, two pignistic transformations (referred to as BetP d/p and BetP f /p ) are constructed, relatively to a location p ∈ RoI, to allow the creation of the probabilities required for decision making. The pignistic transformation (BetP d/p ) of the belief function m Θ t d is represented as follows:

BetP Θ t d/p (θ 0 ) = m Θ t d (θ 0 ) + 1 2 m Θ t d (θ 0 , θ 1 ) BetP Θ t d/p (θ 1 ) = m Θ t d (θ 1 ) + 1 2 m Θ t d (θ 0 , θ 1 ) (3)
Likewise, the pignistic transformation (BetP f /p ) of the bba m Θ nt f is represented as follows:

BetP Θ nt f /p (θ 2 ) = m Θ nt f (θ 2 ) + 1 2 m Θ nt f (θ 2 , θ 3 ) BetP Θ nt f /p (θ 3 ) = m Θ nt f (θ 3 ) + 1 2 m Θ nt f (θ 2 , θ 3 ) (4)
We define the concept of (α,β)-coverage that allows quantifying the quality of coverage delivered by a WSN as follows.

Definition 1. Let α ∈ [0, 1] and β ∈ [0, 1] be two constants, a location p ∈ RoI is (α,β)-covered if:

BetP Θ t d/p (θ 1 ) ≥ α BetP Θ nt f /p (θ 3 ) ≤ β (5)
In [START_REF] Senouci | Fusion-based surveillance wsn deployment using dempster-shafer theory[END_REF], we have demonstrated that the false alarms rate generated by a WSN could be minimized or lessened to zero by assuming the above-described evidence-based fusion approach. We have also shown how this latter can be straightforwardly expanded to handle deployment-related problems such as harsh deployment environments and sensor reliability.

B. Probabilistic-based communication cost model

It is customary to assume a binary connectivity model according to which two sensors are able to communicate directly if the Euclidean distance separating them is less than or equal to a communication range R c [START_REF] Senouci | Deploying Wireless Sensor Networks: Theory and Practice[END_REF]. This binary model simplifies the analysis by approaching the network connectivity problem from a geometric perspective, it remains however limited and not realistic. In fact, empirical research [START_REF] Nikookar | Statistical modeling of signal amplitude fading of indoor radio propagation channels[END_REF] demonstrate that there are no clear-cut boundaries between successful and failed communications.

In practice, the received wireless signal strength is susceptible to noise, interference, and other wireless radio channel impediments. Usually, the variation in received signal strength is characterized in terms of path loss and shadowing. The former describes the amount of wireless signal loss (attenuation) between a receiver and a transmitter whereas the latter is caused by obstacles between the transmitter and receiver that attenuate signal strength through absorption, reflection, scattering, and diffraction.

Empirical measurements have demonstrated that shadowing could be approximated by a zero-mean normal distribution with a standard deviation of σ ǫ . As each environment has unique characteristics, most radio wave propagation models adopt a mixture of empirical and analytical approaches. For a wide range of environments, the log-normal shadowing path loss model [START_REF] Rappaport | Wireless Communications: Principles and Practice[END_REF] is one of the most used radio wave propagation models. It is given by:

P L(d) = P L(d 0 ) + 10γ log 10 ( d d 0 ) + ǫ (6)
where P L(d 0 ) is the path loss (in dB) at a reference distance d 0 , P L(d) is the path loss (in dB) at an arbitrary distance d > d 0 , γ is the path loss exponent (could varies from 2 in free space to 6 inside buildings), and ǫ is a zero-mean Gaussian distributed random variable (in dB) with a standard deviation σ ǫ . This latter is used only when there is a shadowing effect; otherwise, it is zero.

The received signal strength (P r ) at a distance d is usually represented with the following formula:

P r (d) = P t -P L(d) = P t -P L(d 0 ) -10γ log 10 ( d d0 ) -ǫ (7)
Fig. 1 illustrates an analytical propagation model for γ = 2, σ ǫ = 4, P L(d 0 ) = 55dB, d 0 = 1 and an output power P t = 0dBm (e.g., CC2420). According to Equation 7, P r (d) is Gaussian where P r (d) ∼ N (P t -P L(d 0 ) -10γ log 10 ( d d0 ), σ ǫ ). Considering two sensors s i and s j located at distance d from each other, the probability of a successful transmission between s i and s j can be easily calculated as follows:

P[P r (d) > SS min ] = Q SS min -(P t -P L(d 0 ) -10γ log 10 ( d d0 )) σ ǫ (8)
A transmission is considered successful if its received signal strength is greater than a certain threshold SS min which is the minimum acceptable signal strength. Q(.) denotes the complementary cumulative distribution function (CCDF) of a standard Gaussian random variable:

Q(x) = 1 √ 2π +∞ x e -t 2 2 dt
Hence, for a successful communication between s i and s j , the expected number of retransmissions nRT is:

nRT (d) = 1 P[P r (d) > SS min ] (9)
Fig. 2 illustrates the connectivity model formulated above. It clearly shows that in the connectivity range, the received signal strength by some areas is lower than SS min . Whereas, outside the connectivity range, the received signal strength by some area is higher than SS min . As stated before, this model captures the fact that there are no clear-cut boundaries between successful and failed communications. On the basis of the connectivity model described above, we can define the communication cost of a link and by extension that of a cluster as follows.

Definition 2. The expected number of retransmissions (denoted nRT ) required for a successful transmission between two nodes s i and s j represents the communication cost of the link ij (hereafter denoted Lc ij ), given by:

Lc ij = nRT (||ij||) = 1 P[P r (||ij||) > SS min ] Definition 3.
The summation of all communication cost of the links connecting the cluster members to the clusterhead (denoted h) represents the cluster's communication cost (hereafter denoted Cc), given by:

Cc h = si∈ cluster members Lc ih

IV. PROBLEM FORMALIZATION

This section formalizes the uncertainty-aware cluster-based WSNs deployment problem while considering the evidence-based sensing model and the communication cost model, both described in the previous section.

A. Network model and assumptions

The set T ⊆ RoI is defined by the locations of the targets/events that appear in the RoI. These known locations are referred to as target points. T is determined based on the user needs. For instance, target points could be handpicked if a priori information about the possible locations of targets/events is available. Otherwise, target points could be uniformly scattered over the RoI.

The set D ⊆ RoI is defined by the locations that could host the sensors. These locations are referred to as deployment points. We assume that, for each target point t ∈ T, only a subset of deployed sensors (hereafter denoted N(t)) participate in the fusion process. N(t) ⊆ D is a design parameter, which is determined by the user.

As will be discussed in more detail in Section VI, N(t) is mainly constrained by the communication overhead.

We also assume two user-defined inputs α p and β p associated with each target point p ∈ T. α p is the minimum target/event detection probability threshold, whereas β p is the maximum false alarm rate threshold. In the case of a uniform (α,β)-coverage, only two values α and β are defined for the whole set T.

B. Problem formulation

The uncertainty-aware cluster-based WSNs deployment problem is defined as the problem of determining the minimum number of sensors and their locations such that the set of target points T is (α,β)-covered while considering the evidence-based sensing model presented in Section III-A. Deployment-related issues such as network lifespan and connectivity may be included by considering the probabilistic-based communication cost model defined in Section III-B. In this work, besides the sensing quality, we consider the communication cost and lifespan objectives. Thus, we have to simultaneously optimize sensing quality, communication cost, and network lifespan.

Since transmission consumes more energy than any other process, we have to ensure that our sensor placement has reliable links and the overall number of unnecessary retransmissions is minimized. For that, we have to guarantee that the formed clusters minimize the communication cost as defined in Section III-B. These objectives are competing with each other, and therefore, we have Pareto-optimal solutions. For instance, the (α,β)-coverage objective will tend to scatter the network topology to minimize the sensing overlap, whereas the communication cost objective will favor topologies where sensors are not located too far from each other to minimize communication cost and enhance the network lifespan.

Our aim is to generate a good cluster topology where each sensor can transmit directly to the cluster-head. It should be noted here that the expected communication activities carried out by the cluster-heads would lead to excessive energy consumption. To deal with this heavy energy burden of cluster-heads at least two solutions are likely. The first solution is to deploy cluster-heads that are more energy-rich as compared to the sensor nodes. As the positions occupied by cluster-heads are known, the second solution is to redeploy a cluster-head once its energy level reaches a minimum threshold.

The generated topology should ensure full (α,β)-coverage and satisfies the network connectivity constraint while consuming less energy. Additionally, the sensors in the same cluster should be highly connected, and less connected to the sensors in other clusters. There are other problems to be tackled when using clustering methods, such as the number of orphans (isolated) sensors, the number of orphans cluster-heads, and the cluster size, to name few.

Consequently, besides the sensing quality objective, we look for the optimal network topology that best:

• Reduces cluster-heads number;

• Reduces the orphans sensors number (guarantees that each sensor has at least one cluster-head in its vicinity);

• Reduces the orphans cluster-heads number (guarantees that each cluster-head has some sensors in its vicinity);

• Reduces the overlapping areas of clusters (strives to distribute or select the cluster-heads in such a way that there is a minimum overlapping).

• Reduces unnecessary retransmissions overall number.

Formally, the problem at hand is as follows:

(Cc h ) s.t. BetP Θ t d/p (θ 1 ) ≥ α p , ∀p ∈ T BetP Θ nt f /p (θ 3 ) ≤ β p , ∀p ∈ T x p ∈ {0, 1} , ∀p ∈ D
This formulation improves the cluster connectivity as well as the cluster lifetime, and therefore, the network lifetime.

The position of the sink(s) could be easily considered in this formulation. For instance, the straightforward approach is to minimize the distances between the cluster-heads and the sink(s). It is interesting to note that the issue at hand is a binary nonlinear and non-convex multi-objective optimization problem. In the following, we investigate a multi-objective optimization technique to find the global Pareto-optimal solutions.

V. SENSOR PLACEMENT ALGORITHM

Many conflicting objectives typify the nonlinear and non-convex optimization problem described in the previous section. Consequently, it is far essential to deal with that problem as a multi-objective optimization problem. In such a problem, there is usually no single optimal solution, but rather a set of alternative solutions known as the Pareto-optimal solution set, which is the set of solutions such that attempting to improve any objective function would necessarily worsen the other objective values. Pareto-optimal solutions could be obtained for the problem at hand by using multi-objective optimization methods.

Classical optimization methods are limited in handling multi-objective optimization problems, as they transform the multi-objective optimization problem into a single objective optimization problem to find only a single Paretooptimal solution. In this work, we investigate the multi-objective genetic algorithm (GAs). The advantage of this latter is that it can find the whole Pareto-optimal solutions in a single run [START_REF] Talbi | Metaheuristics: From Design to Implementation[END_REF]. A number of multi-objective GAs were developed in the last few years. Among the existing GAs for effectively dealing with multi-objective optimization problems, the most prominent ones are the Pareto archived evolutionary strategy (PAES) [START_REF] Knowles | The pareto archived evolution strategy: a new baseline algorithm for pareto multiobjective optimisation[END_REF], the Strength Pareto evolutionary algorithm (SPEA-2) [START_REF] Zitzler | Multiobjective optimization using evolutionary algorithms -a comparative case study[END_REF], and the Non-dominated sorting genetic algorithm (NSGA-II) [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: Nsga-ii[END_REF]. It has been shown that NSGA-II can converge to the true Pareto-optimal front while ensuring a good distribution of Pareto-optimal solutions [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: Nsga-ii[END_REF]. Furthermore, the complexity of NSGA-II is lower than that of other multi-objective GAs. For that, on the basis of NSGA-II, we devise a new algorithm to solve our multi-objective optimization problem. In the remainder of this paper, this algorithm will be referred to as MGEBDA (Multi-Objective Genetic Evidence-Based Deployment Algorithm).

A. Problem Representation

In MGEBDA, the number and locations of sensors (members and cluster-heads) are specified by an individual which is a candidate sensor placement. This latter is simply modeled by a bit string of length L = 2|D| where each two bits represent a deployment point p ∈ D with the following meaning: (i) "00" no sensor to be deployed, (ii)

"01" or "10" a regular sensor to be deployed, and (iii) "11" a cluster-head to be deployed. To exploit this linear representation, a transformation from 2D (or even 3D) to 1D space is necessary. For instance, the linear horizontal (or vertical) coding (Fig. 3(a)) is a straightforward transformation. Other transformations such as the Z-order curve and the Hilbert space-filling curve (Fig. 3(b)) could also be applied as they preserve fairly well locality. Fig. 3 shows the binary representation of a placement of two sensors and one cluster-head within a 2D 4 × 4 RoI (here D = RoI) using two transformations.

B. Constraints Handling

In this work, we adopt the idea of the constrained-domination principle [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: Nsga-ii[END_REF] to handle constraints. The idea of this approach is based on a simple modification of the definition of the domination relationship between any two solutions x p and x q .

Definition 4. Given two solutions x p and x q , x p is said to constrain-dominate x q , if any of the following conditions is true:

(i) x p is feasible and x q is not;

(ii) x p and x q are both infeasible, but x p has a smaller overall constraint violation;

(iii) x p and x q are both feasible and x p dominates x q .

The previously-defined constrained-domination principle ensures that any infeasible solution has a smaller nondomination rank than all feasible solutions, which are ranked based on their level of non-domination according to the values of the objective function [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: Nsga-ii[END_REF]. However, between two infeasible solutions, the solution with a lower constraint violation is favored.

C. Genetic Operators

As in NSGA-II, MGEBDA uses the bitwise mutation with a small probability p m . However, unlike NSGA-II that uses the one-point crossover, MGEBDA combines three crossover operators: uniform, two-point, and onepoint crossover (Fig. 4). The frequency with which MGEBDA applies the crossover operators is controlled by the crossover rate p c .

D. Evolution Engine

MGEBDA uses the evolution engine of NSGA-II. Selection can be done based on the crowding distance operator as follows: a sensor placement x p wins the tournament with another sensor placement x q if: (i) x p has higher rank than x q , or (ii) x p and x q have the same rank, but x p has a larger crowding distance than x q .

Regarding the replacement strategy, the elitism is implemented by applying the constrained non-dominating sorting on the union of offspring and parent populations. As a result of this operation, the entire population will be sorted into fronts. The new population for the next generation is filled up with the lower ranking fronts solutions while favoring the ones with the largest crowding distance.

E. Description of MGEBDA

Algorithm 1 outlines the pseudo-code of the proposed sensor placement algorithm.

Algorithm 1 MGEBDA Input: external parameters (D, T, coverage model, ...) and internal parameters (population size N , p m , p c , ...)

Output: Pareto-optimal solutions 1: Initialize the first population (of size N ) using randomly generated sensor placements 2: while (stopping conditions are not met) do 3:

Compute the objective values 4:

Assign rank to sensor placements using the constrained non-dominating criteria ⊲ using Definition 4

5:

Compute the crowding distance of each sensor placement 6:

Apply the evolution engine to select the sensor placements from the population 7:

Produce new sensor placements by employing the genetic operators with their respective probabilities 8:

Apply the evolution engine to create the next population 9: end while 10: Return the population's first front

VI. PERFORMANCE EVALUATION

The effectiveness and efficiency of the proposed deployment approach are evaluated by carrying out numerical simulations and testbed-based experiments.

A. Numerical experiments

In this section, we carry out numerical experiments to assess the performance of the proposed deployment approach. First, MGEBDA performances are analyzed for different criteria settings. Second, we evaluate the impact of the fusion radius on the performance of the proposed deployment approach. Finally, we assess the repercussion of the requested connectivity reliability on the deployment cost. MGEBDA implementation is based on the ParadisEO framework [START_REF] Liefooghe | Paradiseo-moeo: A software framework for evolutionary multi-objective optimization[END_REF]. We consider that the deployment and target points are regularly spaced on a grid, therefore the RoI is a k × k grid. Unless otherwise specified, false alarm and detection requirements are assumed uniform over the RoI, with α = 0.9 and β = 0.01. The simulations parameters are described in Table II.

To evaluate the MGEBDA performance or multi-objective algorithms in general, several metrics appeared in the literature [START_REF] Sarker | Assessment methodologies for multiobjective evolutionary algorithms[END_REF]. However, most of the recent proposals [START_REF] Sarker | Assessment methodologies for multiobjective evolutionary algorithms[END_REF] consider that the global Pareto front of the multi-objective optimization under study is known which is not our case. Furthermore, the few metrics that can be employed when considering the global Pareto front is unknown, such as the spread metrics, only judge the uniformity of solution points over different subregions without pointing out the overall quality of solutions.

To assess the performance of MGEBDA for different parameter settings and for the reasons discussed above, we propose to plot the Pareto fronts to enable an enhanced visual inspection including the locations of the fronts, the number of points in each front, and their distribution. For illustration purpose, the objectives considered in the deployment problem were grouped into two objective functions F 1 and F 2 . The F 1 function measures the deployment cost along with the degree of detection rate constraints dissatisfaction and the degree of false alarm rate constraints dissatisfaction. The F 2 function measures all other objectives. Both functions, F 1 and F 2 , are to be minimized.

1) Impact of the key parameters:

In this section, some experiments are performed to illustrate the impact of a couple of different criterion settings on the MGEBDA performance. Precisely, we analyze the effect of the population size and the number of maximum generations on the MGEBDA performance. For that, first all other criteria are fixed, but the number of maximum generations is increased from 100 to 250. Second, we increase the population size from 100 to 400 while keeping all other parameters unchanged.

Fig. 5 shows one of the ten runs of MGEBDA with different parameters settings. First, this figure shows the ability of MGEBDA to converge to the true Pareto front and to find various solutions in the front. Second, increasing the size of the population and/or the number of maximum generations help MGEBDA to converge very close to the true Pareto-optimal front and maximize the number of elements of the Pareto-optimal set found. For instance, with 100 and 250 generations, MGEBDA finds 35 and 81 Pareto-optimal solutions, respectively. A large population size and/or a large number of maximum generations will undoubtedly raise the convergence of MGEBDA. However, it will require more computations per generation which slows the execution of MGEBDA. It is worth mentioning that for large-scale scenarios, an estimation of the required number of sensors and cluster-heads could speed up the convergence time; this could be achieved by exploiting approaches such as [START_REF] Senouci | Sampling-based selection-decimation deployment approach for large-scale wireless sensor networks[END_REF]. We have also analyzed the effect of these parameters on various RoI. We found a population size of 2 × L and a number of maximum generations of 500 to be a good trade-off.

2) Impact of fusion radius:

As discussed previously, one of the most important design criteria of the fusion model is the user-defined fusion radius, which is essentially constrained by the communication overhead. In this section, various numerical results are given to provide a good understanding of the fusion radius impact. To determine the impact of the fusion radius on the deployment and communications costs, the radius is varied from 2 to 9 in a 20 × 20 RoI. Fig. 6 shows, as a function of the fusion radius, the deployment and communication costs (as stated by Definitions 2 and 3) needed for full uniform (0.9, 0.01)-coverage. It is worth to note that as several Pareto-optimal solutions can be found by MGEBDA, each run the best solution is considered in terms of cost of deployment. Fig. 6 shows the impact of the fusion radius on the performance in terms of deployment and communication costs. Two observations are worth noting. First, when the fusion radius is increased from 2 to 6, the deployment cost rapidly dropped from 114 to 32, and then increases gradually to reach 70 when the fusion radius became larger.

Second, the communication cost increases exponentially with the increase of the fusion radius from 2 to 9. This is due to the fact that with the increase of the fusion radius, more distant sensors pay off the data fusion, leading to an improved sensing quality and a lower deployment cost in terms of both sensors and cluster-heads. Fig. 7 illustrates the network topologies generated by MGEBDA while considering two fusion radii. As can be seen in this figure, a fusion scheme with a fusion radius of 6 uses fewer sensors and cluster-heads as compared to a fusion scheme with a fusion radius of 2. Nevertheless, the information quality of the sensors distant from the target point decreases with the increase of the fusion radius. Therefore, their fusion leads inevitably to inferior detection performance, which increases the deployment cost. Consequently, a longer distance between the sensors and their cluster-head results in a higher communication cost.

3) The effect of the requested connectivity reliability: Through this experiment, we analyze the impact of the requested connectivity reliability on the deployment cost (i.e., the number of deployed sensors and cluster-heads).

For that, in a 20×20 RoI, we vary the minimum acceptable signal strength (SS min ) and we analyze the deployment cost. Table III summarizes the obtained results.

We notice that increasing the requested connectivity reliability does not increase the number of regular sensors.

However, the structure of the generated topology, in terms of clusters distribution, was highly affected. In fact, we can clearly see that increasing the requested connectivity reliability increases the number of cluster-heads and therefore increases the number of clusters. This can be explained by the fact that to ensure a high connectivity reliability, the distances separating sensors members and their corresponding cluster-heads are required to be small in order to guarantee links with good quality which, inevitably, reduce the size of the clusters. Nevertheless, these good links help to reduce the communication cost of the network. To summarize, when increasing the requested connectivity reliability, MGEBDA tends to generate small clusters (in terms of distances separating sensor members and their corresponding cluster-heads).

B. Testbed-based experiments

To more investigate the actual benefit of our proposed deployment approach, we have developed a PIR based wireless sensor network testbed termed as ArduiNet. This motion detection testbed is based on the Arduino platform [32] which is an open-source electronics prototyping platform. In the sequel, the testbed architecture and its components are detailed, along with experimental evaluations. A 2.4m × 4m lab room was used to host our ArduiNet deployment. To do so, a two-dimensional metallic grid was installed on the roof in order to hold the ArduiNet nodes as can be seen in Fig. 9. The intersections of the grid lines are our deployment points (Fig. 9).

Deployment points

ArduiNet nodes

Fig. 9. System architecture.

In the sequel, we discuss the acquired results. We describe how to construct mass functions from the analog PIR Phidgets 1111 0 raw sensory data. Then, we evaluate the performance of ArduiNet as a fusion-based surveillance system enriched with the proposed approach.

2) Constructing mass functions: We employ the simple approach described in [START_REF] Senouci | Fusion-based surveillance wsn deployment using dempster-shafer theory[END_REF] to create belief functions from sensing data. Fig. 10 shows a set of belief functions for the considered PIR sensor performing in our lab room. This sensor returns a measure around 500 when there is no motion. Measures out of the 400 to 600 range correspond to motion detection with a high probability. Before the exploitation of ArduiNet, the set of belief functions is constructed empirically by observing the measures returned during several experiments. During the exploitation phase of ArduiNet, each time the cluster-head receives a measure, it performs a projection on the previously constructed set to acquire the corresponding mass function. For example, if the ArduiNet node returns a measure of 100 (see Fig. 10), then the resulting bba will have three focal sets: m({θ 0 }) = 0.05, m({θ 1 }) = 0.94, and m(Θ) = 0.01.

3) The performance of ArduiNet: As explained previously, the ArduiNet is endowed with the proposed approach to build a fusion-based surveillance system. The experimental performances of this latter are discussed in this section.

The leading idea of the proposed approach is to deploy and use the WSN according to the physical and logical topologies that were established during the pre-deployment phase by the sensor placement algorithm fed with the design objectives. Actually, for different physical and logical topologies, the WSN performances are estimated by simulations before its deployment, and the best possible configuration that meets the user requirements is selected.

After that, the WSN real-world deployment and usage must adhere to the selected topologies. For example, Fig. 11 shows a visualization of a sensor placement outputted by the sensor placement algorithm for the lab room scenario with (0.90, 0.01)-coverage. In the experimental tests, we deploy and use ArduiNet as defined by the MGEBDA's output. We allow a person to walk inside the testbed lab room through several paths at different speeds, and we measure the achieved (α,β)-coverage. As explained above, each cluster-head locally makes the detection decision based on the received measurements. The described experiments are repeated more than five thousand times. Table IV illustrates a summary of the obtained results.

The obtained results show that the achieved detection probability is greater than the requested ones, in both cases.

Moreover, a zero false positive rate is acquired. These results are due to the fact that the devised evidence fusion scheme can remarkably improve (α, β)-coverage through the collaboration of nearby sensors. Furthermore, these experiments were accomplished in an indoor area, thus a very low false positive rate was expected. The results of these additional tests confirm the previously obtained results. The proposed deployment approach manages to achieve the requested user requirements in terms of both detection and false alarm rates.

VII. CONCLUSION

Deployment is of the utmost importance in the process of developing WSNs solutions for real-life applications as it decides the available resources and their configuration for system setup. This, in turn, plays a key role in network performance. In this paper, a robust uncertainty-aware cluster-based deterministic deployment approach has been presented. This work presents a contribution to the current literature by providing a comprehensive deployment approach that considers a set of factors involved in the deployment of WSNs. The considered factors reflect several characteristics of real-world applications such as uncertain sensor measurements, the spatial distribution of sensors, unreliable connectivity, harsh deployment environments, and sensor reliability. The described approach was evaluated by both simulation and testbed experiments. The obtained results show that the proposed approach facilitates the deployment of real-world fusion-based wireless sensor networks while achieving the expected network performances.

Fig. 1 .

 1 Fig. 1. Channel Model, γ = 2, σǫ = 4, Pt = 0dBm.

Fig. 2 .

 2 Fig. 2. 2D visualization of the connectivity model.

Fig. 3 .

 3 Fig. 3. Example of a sensor placement representation.

Fig. 4 .

 4 Fig. 4. Crossover operators used in MGEBDA.

  Pareto frontier with different number of maximum genera-Pareto frontier with different population size.

Fig. 5 .

 5 Fig. 5. Pareto frontier for MGEBDA with different parameters settings.

  Deployment cost.

  Communication cost.

Fig. 6 .

 6 Fig. 6. Costs vs. fusion radius.

Fig. 7 .

 7 Fig. 7. Generated topologies vs. fusion radius.

1 )Fig. 8 .

 18 Fig. 8. An ordinary ArduiNet node.

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Example of a set of mass functions related to the analog PIR sensor Phidgets 1111 0.

  Table I presents a comparative overview of the above-discussed cluster-based deterministic deployment approaches.

TABLE I A

 I COMPARISON AMONG CLUSTER-BASED DETERMINISTIC DEPLOYMENT STRATEGIES.

	Ref.	Fusion scheme	Primary objective	Secondary objective	Constraint	Complexity
	[7]	Value fusion	Maximize detection performance	-	Fixed number of sensors	O(3n 6 + 4n 4 )
	[8]	Decision fusion	Maximize detection performance	-	Fixed number of sensors	O(3n 6 + 4n 4 )
	[9]	Value fusion	Maximize detection performance	Minimize the number of sensors	-	O(e n 2 )
	[9]	Value fusion	Maximize detection performance	Minimize the number of sensors	-	O(n 2 me m ) *
	[16]	Value fusion	Strong barrier coverage	Minimize the number of active	Fixed number of static	O(n 4 )
				sensors	and mobile sensors

* m is the mean number of spots within the impact region.

TABLE III THE

 III EFFECT OF THE REQUESTED CONNECTIVITY RELIABILITY.

	SS min (dBm)	Number of sensors	Number of CHs
	-90	28	5
	-60	27	8
	-50	27	9