El Said

A Nouh

Edwin A Baquero

Lise-Marie Lacroix

Fabien Delpech

Romuald Poteau

Guillaume Viau
email: guillaume.viau@insa-toulouse.fr

Surface-engineering of ultrathin gold nanowires: tailored selfassembly and enhanced stability

Gold nanowires with a mean diameter of 1.7 nm were synthesized by reduction of HAuCl4 in a solution of oleylamine (OY) in hexane. A bilayer of oleylammonium chloride/oleylamine at the surface of the raw nanowires was evidenced by NMR and DOSY experiments. After washing a monolayer of oleylammonium chloride remained at the surface of the nanowires. The oleylammonium chloride layer could be progressively replaced by a phosphine shell as evidenced NMR and Diffusion Ordered Spectroscopy experiment (DOSY) experiments, in good agreement with the adsorption energies given by DFT calculations. The nanowires crystallize into hexagonal superlattices with a lattice parameter that can be tailored depending on the ligand shell. Small angle X-ray scattering showed the following lattice parameters: Au@OY + Cl -(OY) (a = 7.2 nm) > Au@TOPO/OY (a = 6.6 nm) > Au@ OY + Cl -(a = 4.1 nm) > Au@TOP (a = 3.75 nm). This is one of few examples of surface modification of ultrathin nanowires that does not alter their morphology. Moreover, the nanowires coated with phosphines exhibited long time stability (at the opposite of other ligands like thiols) opening the way to more complex functionalization.

Introduction

Ultrathin metallic nanowires and metallic nanocontacts exhibit unique structural [START_REF] Gülseren | Noncrystalline Structures of Ultrathin Unsupported Nanowires[END_REF]2 and electronic [START_REF] Requist | Magnetic and Molecular Nanocontacts[END_REF] properties due to their very small diameter and 1D feature. Different ways of elaboration of these nanostructures were developed to measure experimentally quantum properties at room temperature. [START_REF] Requist | Magnetic and Molecular Nanocontacts[END_REF]4 Bottom-up synthesis routes lead to various ultrathin nanowires with applications in different fields like superconducting materials, catalysis or sensors. 4 In particular, ultrathin gold nanowires (Au NWs) are promising candidates for nanoelectronics, 5,[START_REF] Pud | Features of Transport in Ultrathin Gold Nanowire Structures[END_REF] as efficient electro-catalysts for the reduction of CO2 to CO, [START_REF] Zhu | Active and Selective Conversion of CO2 to CO on Ultrathin Au Nanowires[END_REF] as active materials in chemical sensors, [START_REF] Muratova | Chemiresistors Based on Ultrathin Gold Nanowires for Sensing Halides, Pyridine and Dopamine[END_REF] or in optics with longitudinal surface plasmon resonance located in the infra-red region depending on their aspect ratio. [START_REF] Takahata | Surface Plasmon Resonance in Gold Ultrathin Nanorods and Nanowires[END_REF] Moreover, their very high aspect ratio allows to reach a percolation threshold for very low wires volume fraction which is very interesting for transparent and conductive films. [START_REF] Sánchez-Iglesias | Highly Transparent and Conductive Films of Densely Aligned Ultrathin Au Nanowire Monolayers[END_REF][START_REF] Chen | Giant Metal Superlattice Nanomembranes From Ultrathin Gold Nanowires[END_REF][START_REF] Maurer | Templated Self-Assembly of Ultrathin Gold Nanowires by Nanoimprinting for Transparent Flexible Electronics[END_REF] Ultrathin gold nanowires prepared by wet chemistry method are also a class of flexible 1D nanostructure [START_REF] Yuan | Flexible One-Dimensional Nanostructures: A Review[END_REF] and were used to elaborate flexible devices like pressure sensors [START_REF] Gong | A Wearable and Highly Sensitive Pressure Sensor with Ultrathin Gold Nanowires[END_REF] and flexible supercapacitors. [START_REF] Gong | Self-assembled Ultrathin Gold Nanowires as Highly Transparent, Conductive and Stretchable Supercapacitor[END_REF] Directed assemblies of ultrathin gold nanowires onto surface were developed using different techniques like nano-imprinting, [START_REF] Maurer | Templated Self-Assembly of Ultrathin Gold Nanowires by Nanoimprinting for Transparent Flexible Electronics[END_REF] dielectrophoresis [START_REF] Venkatesh | Directed Assembly of Ultrathin Gold Nanowires over Large Area by Dielectrophoresis[END_REF] and nanoxerography [START_REF] Moutet | Directed Assembly of Single Colloidal Gold Nanowires by AFM Nanoxerography[END_REF] in order to measure wires their intrinsic properties and to master the fabrication of devices with complex architectures.

The synthesis of ultrathin Au NWs were reported in several papers. [START_REF] Halder | Ultrafine Single-Crystalline Gold Nanowire Arrays by Oriented Attachment[END_REF][START_REF] Lu | Ultrathin Gold Nanowires Can Be Obtained by Reducing Polymeric Strands of Oleylamine-AuCl Complexes Formed via Aurophilic Interaction[END_REF][START_REF] Huo | Sub-Two Nanometer Single Crystal Au Nanowires[END_REF][START_REF] Feng | Simple and Rapid Synthesis of Ultrathin Gold Nanowires, their Self-assembly and Application in Surface-enhanced Raman Scattering[END_REF][START_REF] Kang | Size-and Shape-Selective Synthesis of Metal Nanocrystals and Nanowires Using CO as a Reducing Agent[END_REF] In most of them gold chloride (HAuCl4) is reduced either in pure oleylamine or in a solution of oleylamine in a nonpolar solvent. Theoretical study using DFT calculations suggested that the amine adsorption favored the stabilization of the {100} Au facets that could explain the anisotropic growth. [START_REF] You | Theoretical Description of the Role of Amine Ssurfactant on the Anisotropic Growth of Gold Nanocrystals[END_REF] Nevertheless, the yield of nanowires was found much higher when oleylamine was diluted in a solvent rather than in pure oleylamine. [START_REF] Loubat | Ultrathin Au Nanowires: Soft-Templating vs Liquid Phase Synthesis, a Quantitative Study[END_REF] Self-assembly of ultrathin Au NWs into bundles were observed in the mother liquors and the characterization of these bundles by small angle X-ray diffraction evidenced a self-organized bi-layer of oleylamine at the surface of the wires that could also explain the anisotropic growth. [START_REF] Loubat | Growth and Self Assembly of Ultrathin Au Nanowires into Expanded Hexagonal Superlattice Studied by in situ SAXS[END_REF] The structure of the oleylamine bi-layer was found very dependent on the nature of the solvent. [START_REF] Reiser | Multivalent Bonds in Self-assembled Bundles of Ultrathin Gold Nanowires[END_REF] One limitation to the use of ultrathin gold nanowires in devices is their instability. [START_REF] Muratova | Resistance Overpotential" Caused by a Potential Drop along the Ultrathin High Aspect Ratio Gold Nanowire Electrodes in Cyclic Voltammetry[END_REF] Wires breakdown under the beam of the electron microscope is difficult to avoid [START_REF] Kura | Synthesis and Growth Mechanism of Long Ultrafine Gold Nanowires with Uniform Diameter[END_REF] and in some cases revealed single atom chain as transient state. [START_REF] Lacroix | Dynamic HAADF-STEM Observation of a Single-Atom Chain as the Transient State of Gold Ultrathin Nanowire Breakdown[END_REF] Aging in solution leads also to a fragmentation due to Rayleigh instability [START_REF] Takahata | Rayleigh Instability and Surfactant-Mediated Stabilization of Ultrathin Gold Nanorods[END_REF] explaining that the electronic properties measured on assemblies of wires are that of shorter fragments. [START_REF] Loubat | Cotunneling Transport in Ultra-narrow Gold Nanowire Bundles[END_REF] Only very few studies dealt with the stability improvement of the ultrathin gold nanowires prepared by wet chemistry. A silica coating of Au ultrathin wires was developed that improved their thermal stability but also their ageing in solutions at different pH. [START_REF] Imura | Preparation of Silica-Coated Ultrathin Gold Nanowires with High Morphological Stability[END_REF] It was also described that oleylamine concentration plays an essential role in the stability of ultrathin gold nanorods. [START_REF] Takahata | Rayleigh Instability and Surfactant-Mediated Stabilization of Ultrathin Gold Nanorods[END_REF] It is very likely that the nanowire surface chemistry may have a strong impact on their stability and that ligand exchange may modify this stability. While the ligand exchange at the surface of ultra-small gold nanoparticles has been deeply studied with a lot of applications such as functionalization for biology, self-assembly or catalytic properties, [START_REF] Woehrle | Thiol-Functionalized, 1.5-nm Gold Nanoparticles through Ligand Exchange Reactions: Scope and Mechanism of Ligand Exchange[END_REF] there is almost no such studies in case of ultrathin Au NWs. Only one paper showed that the replacement of oleylamine by a long-chain amidoamine derivative as ligand in the synthesis makes the ultrathin gold nanowires water-dispersible. [START_REF] Imura | Water-Dispersible Ultrathin Au Nanowires Prepared Using a Lamellar Template of a Long-Chain Amidoamine Derivative[END_REF] In this paper we report on the ligand exchange at the surface of ultrathin Au NWs and on the characterization of this exchange by NMR and small angle X-ray diffraction.

We show that a ligand exchange has strong consequences on the Au NWs selfassembly and on their stability in solution.

Experimental

Materials

Hydrogen tetrachloroaurate tri-hydrate (HAuCl4, 3H2O) was purchased from Alfa Aesar, oleylamine 80-90% (OY) from Across Organic. Triisopropylsilane (TIPS), trioctylphosphine (TOP), trioctylphosphineoxide (TOPO), hexane and absolute ethanol were obtained from Sigma-Aldrich.

Ultrathin gold nanowires synthesis

Ultrathin gold nanowires (Au NWs) were synthesized according to a protocol adapted from Feng et al. [START_REF] Feng | Simple and Rapid Synthesis of Ultrathin Gold Nanowires, their Self-assembly and Application in Surface-enhanced Raman Scattering[END_REF] . In a typical synthesis, 20 mg of HAuCl4•3H2O (10 mM) was dissolved in a solution containing, 0.68 mL of oleylamine (400 mM) and 3.3 ml of hexane. Then, 1.02 ml (1M) of triisopropylsilane (TIPS) was added to the solution to initiate the reduction process. The solution was kept at 25°C for 24 h without stirring.

Purification protocol

The gold nanowire suspensions were subjected to purification and ligand exchange.

One cycle of purification (1-purif) consisted in the following sequence: 5 mL of absolute ethanol were added to 2.5 mL of the as prepared Au NWs suspension, the mixture was centrifuged at 4000 rpm for 5 min and the supernatant was discarded.

The precipitate was redispered in 2.5 mL of hexane for stability assessment and in 1 mL for SAXS measurements. Two purifications (2-purif) consisted to repeat this cycle once again on the washed suspension.

Ligand exchange

Oleylamine was exchanged by trioctylphosphine (TOP) and trioctylphosphine oxide (TOPO) according to the following protocol. First, 500 µL of the suspension of Au NWS in hexane were washed with ethanol (1mL), centrifuged at 4000 rpm for 5 min and redispersed in 500 µL of hexane. Then, 500 µL of a solution of 10 mM of TOP (or TOPO) were added to the purified Au NWs in hexane. These suspensions were characterized after aging for different times at 25°C. The suspensions were characterized as such and purified following the same procedure as described above.

The TOP solutions were handled in a glove box to avoid the TOP oxidation.

Characterizations

The transmission electron microscopy (TEM) characterizations were performed using a JEOL 1011 microscope operating at 100 kV. A drop of gold nanowire suspension in hexane was deposited on a carbon-coated copper grid and dried under vacuum.

Small Angle X-ray Diffraction was performed on a PANalytical Empyrean diffractometer equipped with a Cobalt source, λ (Co Kα1/Kα2) = 1.7889/1.792Å, a Bragg-Brentano HD optics with a divergence slit of 1/32° and an anti-scatter slit of 1/8°, and a PIXcel1D-Medpix3 detector. Several drops of gold nanowire suspension in hexane were deposited on a zero-background silicon substrate and then dried at room temperature for 3 min.

Solution NMR spectra were obtained on a Bruker Avance I 500 spectrometer equipped with a 5 mm triple resonance inverse Z-gradient probe (TBI 1 H, 31 P, BB). 1 H NMR spectrum were recorded in toluene-d8 at 293 K. Diffusion measurements were made using the stimulated echo pulse sequence. The mixing time of NOESY experiment were set to 100 ms. Chemical shifts (δ, parts per million) are quoted relative to SiMe4 ( 1 H). They were measured by internal referencing to the residual 1 H resonances of the deuterated solvent (toluene-d8, 1 H δ 2.09 as a quintuplet of the methyl group). [START_REF] Loubat | Cotunneling Transport in Ultra-narrow Gold Nanowire Bundles[END_REF] P chemical shifts were referenced to an external 85% H3PO4 sample.

Density Functional Theory calculations

As already done in our previous paper, [START_REF] Loubat | Ultrathin Au Nanowires: Soft-Templating vs Liquid Phase Synthesis, a Quantitative Study[END_REF] the electronic properties of [111] oriented bulk AuNWs were calculated within the framework of the DFT considering periodic boundary conditions and the spin polarized constraint. These [111] direction oriented AuNWs, were generated by cleaving fcc bulk Au with low index surfaces. The exchange-correlation potential was approximated by the generalized gradient approach proposed by Perdew, Burke, and Ernzerhof (PBE). [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] Calculation of the energetic parameters as well as the geometry optimizations were carried out using the projector augmented waves (PAW) full-potential reconstruction [START_REF] Blöchl | Projector Augmented-wave Method[END_REF][START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-wave Method[END_REF] implemented in the Vienna ab initio simulation package, VASP. [START_REF] Kresse | Efficiency of Ab Initio Total-energy Calculations for Metals and Semiconductors Using a Plane-wave Basis Set[END_REF][START_REF] Kresse | Efficient Iterative Schemes for Ab Initio Totalenergy Calculations Using a Plane-wave Basis Set[END_REF] To minimize errors arising from the frozen core approximation, we used the PAW data sets treating the 4p, 4d and 5s Au states (17 valence electrons). A kinetic energy cutoff of 525 eV was sufficient to achieve a total energy convergence within several millielectronvolts for ligands adsorption. van der Waals interactions were taken into consideration by adding a pairwise interatomic term Edisp to the Kohn-Shan DFT energies, which was evaluated using the revised DFT-D3 method of Grimme with Becke-Jonson damping. [START_REF] Grimme | A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu[END_REF] , [START_REF] Grimme | Effect of the Damping Function in Dispersion Corrected Density Functional Theory[END_REF] For the geometry optimizations, a (1×1×11) Γ-centered [42] k-points grid was used to sample the reciprocal space combined with a Gaussian smearing of 0.02 eV width for the partial occupancies. Atoms were free to move until the residual forces on any direction were less than 0.02 eV/Å. The supercell size along the a and b directions is set to ensure a vacuum space of ca. 14 Å between periodic images of decorated Au NWs.

Results and Discussion

Au NWs characterizations

Figure 1 shows a TEM image of Au NWs prepared by the reduction of HAuCl4•3H2O dissolved in a solution of oleylamine in hexane with TIPS at 25°C. The wire mean diameter is d = 1.7 nm and the standard deviation of the diameter distribution is very small as already observed by several studies. [START_REF] Feng | Simple and Rapid Synthesis of Ultrathin Gold Nanowires, their Self-assembly and Application in Surface-enhanced Raman Scattering[END_REF][START_REF] Loubat | Growth and Self Assembly of Ultrathin Au Nanowires into Expanded Hexagonal Superlattice Studied by in situ SAXS[END_REF] Several drops of a suspension in hexane of Au NWs purified one time were evaporated on the XRD zero background silicon substrate. The X-ray diffraction pattern of the dry assembly exhibited several peaks at small angles revealing the crystallization of the NWs in a hexagonal phase.

The peak positions in the reciprocal space relative to the position of the first peak were 1:√3:√4:√7:√9:√12:√13 (Fig. 2a) characterizing a bidimensional hexagonal positional order in the plane normal to the wires. The lattice parameter a calculated as the average of the distance of the different (hk) reflections ( ) = √ was found equal to 7.2 nm. In such hexagonal array the parameter a corresponds to the inter-wire distance. [START_REF] Loubat | Growth and Self Assembly of Ultrathin Au Nanowires into Expanded Hexagonal Superlattice Studied by in situ SAXS[END_REF] The spacing between the wires is thus estimated to e = ad = 5.5 nm (with d the wire diameter of 1.7 nm). Additional peaks corresponding to the (00l) reflections of pure oleylamine were also observed (Fig. 2a)

showing an excess of OY that crystallized on the substrate at room temperature.

The XRD pattern at small angles of the same nanowires purified twice revealed also the formation of a hexagonal phase but with (hk) reflections strongly shifted to high q (Fig. 2b). This shift reveals a much smaller lattice parameter a = 4.1 nm and a corresponding spacing between the wires e = ad = 2.4 nm. The peaks of pure oleylamine did not appear on the XRD pattern in agreement with an efficient washing that removed the free oleylamine molecules from the suspensions purified twice (Fig. 2b).

Previous studies described the self-assembly of ultrathin Au NWs into hexagonal phase in solution. In situ small angle X-ray scattering experiments carried out on assynthesized suspensions showed the formation after a few hours of a hexagonal phase with a lattice parameter a = 9.7 nm. [START_REF] Loubat | Growth and Self Assembly of Ultrathin Au Nanowires into Expanded Hexagonal Superlattice Studied by in situ SAXS[END_REF] This very large parameter compared to the oleylamine length in all-trans configuration (2.1 nm) was explained by a bi-layer of oleylamine around the Au NWs. Recently, Reiser et al. showed that the lattice parameter of the Au NWs hexagonal phase that crystallized in the mother liquor strongly depends on the oleylamine volume fraction in the solution. They found a variation between 10.2 nm and 7.5 nm when the OY volume fraction was varied between 0.05 and 0.75, respectively. [START_REF] Reiser | Multivalent Bonds in Self-assembled Bundles of Ultrathin Gold Nanowires[END_REF] This variation was interpreted as the result of a progressive interdigitation of the OY molecules surrounding the wires due to an increasing osmotic pressure when the concentration of free OY was increased. [START_REF] Reiser | Multivalent Bonds in Self-assembled Bundles of Ultrathin Gold Nanowires[END_REF] The lattice parameter of 7.2 nm measured on the dried nanowires is in good agreement with this variation. In the present case hexane was evaporated that could provoked an even stronger interdigitating. Nevertheless, the large interwire spacing (5.5 nm) compared to the length of a single OY molecules supports that the Au NWs after one purification are still coated by a bilayer of oleylamine molecules with a strong interdigitation.

After two purifications the shortening of the distance between the wires in the hexagonal phase can be explained by the removal of the external layer of OY leading to a single OY layer at the surface of the wires. Considering that OY has a length of 2.1 nm in all-trans configuration, the spacing of 2.4 nm means that the OY molecules strongly interdigitate. A scheme of the interwire spacing in the different distance hexagonal phases is proposed on figure 10. Suspensions of Au NWs after one and two purifications were characterized by solution [START_REF] Gülseren | Noncrystalline Structures of Ultrathin Unsupported Nanowires[END_REF] H NMR spectroscopy in toluene-d8. In the spectrum of the sample purified one time resonance signals were found at 5.51, 2.55, 1.45, 1.35-1.15, and 0.95 ppm that are attributed to the alkene, the CH2 alpha to the NH2, the CH2 beta to the NH2, the 13 CH2 and the methyl groups of oleylamine, respectively (Fig. 3a). The Diffusion Ordered Spectroscopy experiment (DOSY) gave a diffusion coefficient of 1.0 10 -9 m 2 .s -1 . This value is similar to that found for pure OY (1.1 x 10 -9 m 2 .s -1 , Fig. S1) and it is thus attributed to free OY due to the large excess present in the suspension in agreement with the results found by SAXS.

(a) (b)

In the 1 H NMR spectrum of the Au NWs purified twice the resonance signal attributed to the CH2 alpha and beta to the NH2 group were shifted to 2.82 and to 1.79 ppm, respectively (Fig. 3b). This downfield shift compared to the resonance signals of the free OY is attributed to the presence of oleylammonium chloride in the sample that was not detectable in the sample purified only one time. The presence of oleylammonium was confirmed by the resonance signal centered at 8.85 ppm assigned to the -NH3 + cation (Fig. 3b). Moreover, the resonances of the CH2 alpha and beta to the NH3 + group are broadened revealing the coordination of the oleylammonium to the Au NWs surface. Indeed, the reduced mobility of the ligands bound to a nanoparticle induces the NMR lines broadening and this effect is more marked for the protons closest to the surface. [START_REF] Marbella | NMR Techniques for Noble Metal Nanoparticles[END_REF][START_REF] Cros-Gagneux | Surface Chemistry of InP Quantum Dots: a Comprehensive Study[END_REF][START_REF] Ramirez | Shape Control of Platinum Nanoparticles[END_REF][START_REF] Ramirez | Influence of Organic Ligands on the Stabilization of Palladium nanoparticles[END_REF] Additionally, a confirmation of the coordination of oleylammonium to Au NWs is given by the diffusion coefficient measurements obtained from DOSY experiments (Fig. S2). Whereas the diffusion coefficient found for free OY in this sample was 8.9 10 -10 m 2 .s -1 , the oleylammonium displayed a significant lower value (4.0 10 -10 m 2 .s -1 ).

The presence of oleylammonium is probably due to the presence of an acid proton in the gold precursor HAuCl4, 3 H2O. Previous theoretical calculations suggested that that the adsorption of ammonium chloride was more favorable than amine at the surface of gold nanowires. [START_REF] Loubat | Ultrathin Au Nanowires: Soft-Templating vs Liquid Phase Synthesis, a Quantitative Study[END_REF] The modification of the ligand shell with washing suggests a first coordination shell containing mainly the ammonium and a second shell containing mainly the amine. In the sample washed only one time the excess of free amine hides the signal of the ammonium shell.

Ligand exchange

A solution of trioctylphosphine (TOP) in hexane (10 mM) was added to a dispersion in hexane of nanowires purified one time (gold concentration = 10 mM). X-ray diffraction patterns at small angle were recorded at different times after the addition of TOP. Several drops of the suspension were deposited and dried on the zerobackground Si substrate. On figure 4 are given the XRD patterns recorded after a contact time between the wires and TOP of 30 min and 72h. In both cases the wires crystallize in a single hexagonal phase with a lattice parameter significantly lower than the lattice parameter of 7.2 nm measured on the purified nanowires coated by oleylamine. The observation of a single phase, and not a mixture of two phases, is consistent with a progressive ligand exchange in the NW coordination shell, the lattice parameter being a mean value of the interwire distances. After only 30 min of contact time the lattice parameter was found a = 4.85 nm (Fig. 4a) and after 72h it decreased to reach a = 3.75 nm (Fig. 4b).

The same experiments were done with trioctylphosphine oxide TOPO (Fig. 5). The wires crystallized in a hexagonal phase with a lattice parameter significantly higher than with TOP, a = 6.6 nm, and that did not vary when the time was increased from 30 min to 72 h. In order to follow the coordination of TOP and TOPO ligands at the surface of the Au NWs, solution NMR analysis were performed after ligand exchange and after different cycles of purification.

After the addition of TOP, a resonance signal centered at -32.3 ppm was detected in the 31 P NMR spectrum. This peak was assigned to free TOP. After one and two purifications, this resonance was not detected anymore by solution [START_REF] Loubat | Cotunneling Transport in Ultra-narrow Gold Nanowire Bundles[END_REF] P NMR spectroscopy (Figure S3) meaning that free TOP was no more present in the sample.

The same result was found when the ligand exchange was made with TOPO. After either one or two purifications, no free TOPO (δ 42.4 ppm) was detected by [START_REF] Loubat | Cotunneling Transport in Ultra-narrow Gold Nanowire Bundles[END_REF] P NMR (Figure S4). In the 1 H NMR spectra of the samples treated with TOP after both, one and two purifications, the resonance signal centered at 1.6 ppm is attributed to the CH2 group in alpha to the phosphorous atom indicating the presence of TOP at the surface of the wires. The resonance signal is broadened and slightly shifted to higher frequencies compared to the same resonance signal in the free TOP (1.5 ppm) due to the coordination of TOP to the wires (Figure 6b, c andd). Interestingly, the signal of oleylammonium is no more present suggesting the full replacement of this ligand by the phosphine. Additionally, the peaks at 5.51 and 2.55 ppm assigned to the alkene and the CH2 alpha to the NH2 of OY are also detected and this confirms the residual presence of OY as observed by SAXS. Consistently, the DOSY experiments evidenced two diffusion coefficients in the sample purified twice, 1.4 x 10 -9 m 2 .s -1 and 2.2 x 10 -10 m 2 .s -1 . The first coefficient is assigned to free OY while the second is assigned to coordinated TOP since the diffusion filtered spectrum at 2.2 x 10 -10 m 2 .s -1

only shows the resonances of TOP (Fig. S5). These results together with those obtained by [START_REF] Loubat | Cotunneling Transport in Ultra-narrow Gold Nanowire Bundles[END_REF] P NMR suggest that TOP has replaced oleylammonium and is tightly bound to the surface of Au NWs. This is confirmed by periodic-DFT calculations, aiming at evaluating the adsorption energy of surface species on a 1.7 nm Au NW.

The results are summarized in Figures 10 andS6. As already explained in Ref. 24, the methylammonium chloride ion pair, with the polar ammonium head lying above an adsorbed chloride, binds weakly at the Au NW surface (-19.1 kcal.mol -1 ), whereas its adsorption is significantly enhanced if both moieties are simultaneously adsorbed.

Such adsorption can result in an alternant positive/negative pattern that enhances adsorption strength (-40.1 kcal.mol -1 per ion pair). Regarding the adsorption of TOP, we considered a smaller molecular model, PMe3, in order to reduce the computational effort. Such model provides a lower limit of the adsorption strength of σ-donor phosphines. It turns out that the σ-donor character of the trimethylphosphine ligand is already strong, with an adsorption energy of -43.4 kcal.mol -1 , 20 kcal.mol -1 stronger than the adsorption of the trimethylamine counterpart (a detailed comparison of the electronic structure of grafted amines and phosphines is given in the supporting information document. In short, a smaller HOMO-LUMO gap in PMe3 and a significant ligand-to-metal charge transfer interaction observed when grafted to the metal surface, account for a stronger adsorption energy). This result suggests that the surface adsorption of TOP on AuNW surface is a thermodynamic driving force that breaks the ionic interactions and that explains the exchange between ammonium and TOP ligands.

The progressive decreased of the interwire distance is explained by a progressive substitution of the OY by TOP that exhibit shorter chains. Au NWs aged 72 h with TOP crystallized in a hexagonal phase with a very short lattice parameter of 3.75 nm corresponding to an interwire spacing of only 2 nm, i.e. lower than the oleylamine length. This value suggests a nearly complete exchange of OY by TOP (Fig. 10).

Regarding to the Au NWs treated with TOPO, in the 1 H NMR spectra of the samples after one and two purifications, the resonances of oleylammonium are again lacking while those of OY and TOPO can be observed. The signal at δ = 1.6 ppm attributed to the CH2 group in alpha to the phosphorous atom was broadened compared to free TOPO (Fig. 7b, c andd), suggesting that TOPO is coordinated to the surface. The presence of TOPO molecules in the first coordination shell was confirmed by DOSY experiments. Two diffusion coefficients were found, 9.1 10 -10 m 2 .s -1 and 1.29 10 -10 m 2 .s -1 , attributed respectively to OY and TOPO thanks to the diffusion filtered spectrum (Fig. S7). However, in contrast to the sample treated with TOP, the signals of the alkene and CH2 alpha to NH2 of OY are slightly more intense in the sample treated with TOPO (Fig. 7a,d) suggesting a less efficient exchange with TOPO than with TOP. A larger amount of oleylamine remaining in the coordination shell of the NWs could explain a larger interwire distance. With TOPO the lattice parameter of the NW array after 72 h takes an intermediate value between the parameter measured on the nanowires coated by oleylammonium chloride oleylamine and those after TOP exchange. This suggests that the oleylamine exchange is incomplete with TOPO while almost complete with TOP. This finding can be rationalized in terms of hard-soft acid-base (HSAB) principle. [START_REF] Pearson | Absolute Electronegativity and Hardnes: Application to Inorganic Chemistry[END_REF] Au nano-objects with soft surface sites form stronger bond with the soft P atom (i.e. TOP) than with the hard O atom (i.e. TOPO).

Au NWs stability

The stability of the nanowires in solution was followed by examining the evolution of morphology by TEM and superlattices formation by XRD during 13 days. On Figure 8 are presented the SAXS pattern and the corresponding TEM images of Au NWs purified one time and aged in solution for different time intervals. After 7 days one can notice that the peak intensity of the NW hexagonal array decreased and the superlattice disappeared completely after 13 days, peaks corresponding to pure oleylamine only remain (Fig. 8c). The full width at half height, ∆q, of the (10) peak reported in table 1 showed a progressive broadening with time meaning that the coherence length of the hexagonal array, estimated to Lcoh = 2π/∆q, decreased continuously. The TEM images showed that the mean diameter of the Au wires increased after 7 days that explained the loss of coherence of the hexagonal lattice. After 13 days the ultrathin NWs totally disappeared. Anisotropic particles were still observed but their mean diameter increased to a mean value of 11 nm with a large size distribution and no long range order was visible in agreement with the SAXS pattern. Phosphines are good ligands to preserve the NW morphology and to improve their stability with time in solution. At the opposite when we tried to make ligand exchange with 1-dodecanthiol, we found that this ligand destroys the Au NWs even at low concentrations (Fig. S8).

Summary and conclusion

Gold ultrathin nanowires (Au NWs) with a mean diameter of 1. Au@TOPO/OY (a = 6.6 nm) > Au@Cl -OY + (a = 4.1 nm) > Au@TOP (a = 3.75 nm).

The two first values are explained by a bilayer of ligand at the surface of the Au NWs while the two last values are explained by a monolayer (Fig. 10) in agreement with the DOSY experiments.

In conclusion we have showed that it is possible to tailor the interwire distance of ultrathin gold nanowires in hexagonal array playing on the ligand shell. This study showed also that Au NWs coordinated by TOP and TOPO exhibit long time stability in solution which is an important prerequisite for further applications and it opens the way to more complex functionalization.

Theoretical part: analysis of the DFT electronic structure

This part aims at evaluating the Au-LMe3 interaction (L=P or N) thanks to the molecular orbital language. Since the states calculated with VASP are expanded in a plane wave basis set, it is necessary to project them on a local basis set. This is achieved with the LOBSTER (Local Orbital Basis Suite Towards Electronic-Structure) package [1]. According to the DOS and COHP profiles, the Au-P bonding state located at ca. -12 eV has a strong charge transfer (CT) character, with a small component on the neighboring gold atom (blue and maroon DOS profiles), that does not exist in the naked AuNW (see DOS profile in Fig. S9). Other states higher in energy also significantly contribute to the bonding between Au and the PMe3 ligand, whereas the states close to the fermi energy (EF) exhibit an antibonding character. Nevertheless, the integration of COHP(ε) up to the Fermi energy indicates a net bonding interaction (ICOHP: 2.0 eV, i.e. 45 kcal/mol). An Au-Au interaction is much weaker, with ICOHP: 0.3 eV (7.6 kcal/mol, but mind that the coordination number of gold atoms is in the range 5 to 12). The electronic population per atom can be calculated by integrating the DOS up to the Fermi energy. The gross population on P is 4.5e, whereas the gross population on each methyl group is 7.8e, probably owing to some back-donation from the surface.

Figure 1 .

 1 Figure 1. TEM image of Au NWs synthesized by reduction with TIPS of a solution of HAuCl4•3H2O in a solution hexane containing oleylamine at 25°C for 24 h.

Figure 2 .

 2 Figure 2. X-ray diffraction pattern at small angles of Au NWs deposited and dried on a zero-background silicon substrate (a) wires purified one time and (b) wires purified twice.

Figure 3 .

 3 Figure 3. 1 H NMR spectra of Au NWs coated by oleylamine/oleylammonium shells after (a) one purification and (b) two purifications (*:toluene-d8, □: water).

Figure 4 .

 4 Figure 4. X-ray diffraction patterns at small angle of Au NWs aged in a solution of TOP for different times: (a) 30 min ; (b) 72 h. (*OY peaks are marked with a star).

Figure 5 .

 5 Figure 5. X-ray diffraction patterns at small angle of Au NWs aged in a solution of TOPO for different times: (a) 30 min ; (b) 72 h.

Figure 6 .

 6 Figure 6. 1 H NMR spectra of (a) oleylamine, (b) trioctylphosphine, (c) Au NWs coated by oleylamine exchanged with TOP after one purification, and (d) after two purifications (*:toluene-d8, □: water).

Figure 7 . 1 H

 71 Figure 7. 1 H NMR spectra of (a) oleylamine, (b) trioctylphosphine oxide, (c) Au NWs coated by oleylamine exchanged with TOPO after one purification, and (d) after two purifications (*:toluene-d8, □: water).

Figure 9

 9 Figure 9 shows the effect of aging on SAXS measurements and the corresponding TEM images of Au NWs stabilized by TOP and TOPO. Even after 13 days of aging in solution the Au NWs kept their morphology and the hexagonal arrays were still observed by SAXS. The peak broadening observed for short contact time with TOP and TOPO compared to the original hexagonal array (Tab. 1) is likely due to parameter fluctuations due to the progressive shell replacement of oleylammonium chloride by the phosphines. After 3 days of contact time this peak broadening is stabilized showing the absence of any further evolution.

Figure 8 .

 8 Figure 8. Effect of time on Au NWs prepared at 25 °C: SAXS patterns after 0, 7 and 13 days (a, b, c) and corresponding TEM images (d, e, f).

Figure 9 .

 9 Figure 9. Effect of time on Au NWs after TOPO and TOP ligand exchange: SAXS measurements after 3 and 13 days (a, b)with TOPO, and (c, d) with TOP; corresponding TEM images after 3, 13 days (e, f) TOPO and (g, h) TOP.

Figure 10 .

 10 Figure 10. Schematic representations of the ligand shell of Au NWs and interwire distance: (a) after 1 purification ; (b) after 2 purifications and (c) after exchange with TOP. Right: adsorption energies of methyl ammonium chloride and trimethylphosphine calculated by periodic-DFT.

  7 nm were synthesized by reduction of HAuCl4 in a solution of oleylamine in hexane. The oleylamine (OY) was then exchanged by trioctylphosphine (TOP) and trioctylphosphine oxide (TOPO).SAXS and NMR characterizations were carried out on the Au NWs in dried state and in solution, before and after ligand exchange.Hexagonal arrays of parallel nanowires were evidenced by SAXS. This technique presents the advantage over transmission electron microscopy to characterize large amount of samples and not only local area. The formation of hexagonal arrays of nanowires requires monodisperse wires and well-defined ligand shell. The lattice parameter of the hexagonal arrays gives the mean interwire distance and the spacing between the wires is calculated by subtracting their mean diameter. We observed that the lattice parameter decreased when oleylamine was removed by washing and the interwire distances are consistent with wires coated by a bilayer of oleylamine that becomes a monolayer after washing.[START_REF] Gülseren | Noncrystalline Structures of Ultrathin Unsupported Nanowires[END_REF] H NMR allowed to precise that the first coordination shell consisted mainly in oleylammonium suggesting the presence of chloride ions bound to the gold surface in agreement with adsorption energy calculations by periodic DFT.The oleylamine/oleylammonium bilayer was modified by ageing nanowires suspensions in TOP and TOPO solutions in hexane. NMR showed that the oleylammonium chloride shell was completely removed by TOP and TOPO. This experimental result was confirmed by DFT calculation showing a stronger adsorption of phosphines on the Au NWs. NMR showed also that OY molecules remained with TOPO while they were almost completely replaced by TOP. The ligand shell modification changed the lattice parameter of the NWs hexagonal arrays. The following order of the lattice parameters was found: Au@Cl -OY + (OY) (a = 7.2 nm) >

Figure S6 .

 S6 Figure S6. Adsorption energies (in kcal.mol -1 ) and patterns of ligands on a gold nanowire.

Figure S7 .

 S7 Figure S7. Diffusion filtered 1 H NMR spectrum of Au NWs treated with TOPO after two purifications. The spectrum corresponds to the resonance signals observed at D = 1.29 x 10 -10 m 2 s -1 .

Figure S8 .

 S8 Figure S8. (a) SAXS pattern of Au NWs after ligand exchange with 1-dodecanthiol; (b) corresponding TEM image.

Figure S9 .

 S9 Figure S9. MOs of LMe3 (L=P or N), calculated at the DFT-B3LYP level of theory, with the Gaussian09 package [4], within the 6-31G(d,p) basis set. The occupied MOs that are expected to be involved in the Au-LMe3 interactions due to their significant L-axial and Ltangential character are marked with a * sign. Although the HOMO lies at the same energy in both ligands, the lone pair-like component is more diffuse on P than on N. With a slightly more stable LUMO in PMe3 than in NMe3, the HOMO-LUMO gap is smaller in the phosphine ligand, in line with its softer HSAB character. The other occupied MOs than can be involved in the surface-ligand interactions lie closer to the Fermi energy in PMe3 than in NMe3. Overall, these features are expected to involve a stronger interaction of the phosphine with the surface.

Figure S10 .

 S10 Figure S10. pDOS and pCOHP profiles for the bare AuNW (LOBSTER basis set on which the projection is done: 5p, 5d, 6s. Absolute charge spilling: 1.65%. This small charge spilling is not significantly reduced by adding a 6p subshell in the basis set). εd and εs designate the d-and s-band centers, following the seminal d-band center formulation of Hammer and Nørskov [5]. The atomic population is calculated by integration of the projected DOS. It is no surprise that it is in line with the Au(0) character of gold atoms in this bare metal nanowire.

Figure S11 .

 S11 Figure S11. pDOS and pCOHP profiles for PMe3*AuNW. The s-and d-band centers for the gold nanowire do not change much upon adsorption with respect to the bare AuNW.

Table 1 .

 1 Effect of time on Au NWs stabilized by oleylamine and after TOP and TOPO ligand exchange on the FWHM (∆q) of the (10) peak. For the pure oleylamine shell the corresponding coherence length L=2π/∆q is given.

	Time	OY		TOP	TOPO
	(day)	∆q (nm -1 )	L (nm)	∆q (nm -1 ) ∆q (nm -1 )
	0	0.085	75	0.13	0.14
	3	0.24	26	0.25	0.13
	9	0.34	18	0.26	0.13
	13	-	-	0.26	0.13

  It allows calculating Crystal Orbital Hamilton Population (COHP, see Ref. 2) curves projected in a local atomic basis set (pCOHP), and also reliable atom-projected density of states (pDOS), both directly based on plane-wave wavefunctions calculated with the VASP package. Several example of the application of such analysis to ruthenium nanoclusters in equilibrium with syngas can be found in Ref. 3.

Acknowledgement E. S. A. Nouh thanks the French Institute in Cairo (Egypt), the Science and Technology Fund (STDF) and Institut National des Sciences Appliquées of Toulouse for awarding a Fellowship to support this research. E. S. A. Nouh gratefully acknowledges the help from Egyptian Nuclear Materials Authority (Cairo) for granting him a sabbatical leave to carry out this work at LPCNO. E.A.B. is grateful to Marie Curie Actions and Campus France for a PRESTIGE post-doc fellowship (FP7/2007-2013) under REA grant agreement n° PCOFUND-GA-2013-609102. This work was supported by Programme Investissements d'Avenir under the program ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT. We thank Yannick Coppel and Christian Bijani for NMR measurements. R. Poteau also acknowledges the CALcul en MIdi-Pyrénées HPC (CALMIP-EOS, grant P0611) for its generous allocation of computational resources.

profile, the states lying at -12.5 eV and -16 eV are localized on the ligand, with no significant contribution of the metal that could favor a LMCT state. Other states higher in energy significantly contribute to the bonding between Au and the NMe3 ligand, whereas the states close to the fermi energy (EF) exhibit an antibonding character. The integration of COHP(ε) up to the Fermi energy indicates a net bonding interaction weaker than PMe3 at the same site (ICOHP: 0.8 eV, i.e. 19 kcal/mol). The Au-Au interaction is still characterized by a weak ICOHP index: 0.3 eV (7.6 kcal/mol). The electronic population per atom can be calculated by integrating the DOS up to the Fermi energy. The gross population on N is much higher than calculated on P (5.7e vs. 4.5e), whereas the gross population on each methyl group is 7.5e. Overall, these results show a weaker LMCT charge transfer in the amine-protected AuNW.


Olivier Varenne

Thomas Cuisset

Aurès Chaïb

Marie-Claude Morice

Manel Sabaté

Tian-Hai Koh

Isabelle Durand-Zaleski

Olivier Hanon

Kris Bogaerts

Peter Sinnaeve

Olivier Varenne1

PhD Thomas Cuisset3

PhD Aurès Chaïb1

MD Marie- Claude Morice4

MD Manel Sabaté5

MD Tian-Hai Koh6

MD Isabelle Durand-Zaleski7

PhD Olivier Hanon2

MD, PhD Kris Bogaerts9

PhD; Peter Sinnaeve11

The SYNERGY II Everolimus elutiNg stent In patients Older than 75 years undergoing coronary Revascularisation associated with a short dual antiplatelet therapy (SENIOR) trial: rationale and design of a large-scale randomised multicentre study

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

Introduction

Despite age being a strong predictor of major adverse cardiac and cerebrovascular events (MACCE) after percutaneous coronary intervention (PCI)1,2, elderly patients have been largely excluded, under-represented or highly selected in randomised trials evaluating drugeluting stents (DES). However, DES implantation in elderly patients could lead to a significant reduction in the rate of myocardial infarction (MI) and target vessel revascularisation compared to bare metal stent (BMS) implantation3.

New-generation DES have been demonstrated to be safer compared to first-generation DES4,5. In the Patient Related OuTcomes with Endeavor vs. Cypher stenting Trial (PROTECT), Camenzind et al reported a strong interaction between DES types and dual antiplatelet therapy (DAPT) use, suggesting different vascular healing responses according to the type of DES6. More recently, in order to limit the potential long-term harm and toxicity associated with durable polymers7, DES with bioresorbable polymers have been developed8,9. Whether or not DES with a biodegradable polymer are safer than DES with a durable polymer is still a matter of debate10,11. However, Stefanini et al reported a lower risk of stent thrombosis and MI at four years with a biodegradable polymer DES in a pooled analysis including 4,062 patients12.

There is emerging evidence that reducing the duration of DAPT together with new-generation DES could represent a safe strategy. This might be particularly relevant for patients ≥75 years old, to reverse the unfavourable risk/benefit ratio associated with earlier-generation DES and long DAPT. Despite European Society of Cardiology and American Heart Association/American College of Cardiology guidelines recommending 12 months of DAPT13,14,15, the optimal duration of DAPT after DES implantation remains largely unknown, particularly in patients ≥75 years old. Bleeding risk is higher in elderly compared to younger patients16, and is further increased with longer DAPT17,18,19 without clear reduction in stent thrombosis in several studies17,19,20. The potential impact of bleeding complications may explain why cardiologists are often reluctant to expose patients ≥75 years old to prolonged DAPT and why BMS are often preferred for PCI in these patients. Indeed, in a very recent registry from two reputable European centres, only about one out of four consecutive elderly patients undergoing PCI received at least one DES21.

Several trials have reported similar efficacy and safety with short vs. long DAPT duration after PCI (Table 1). Three months of DAPT was non-inferior to 12 months of DAPT with respect to the occurrence of stent thrombosis or MACCE in the RESET (REal Safety and Efficacy of three-month dual antiplatelet Therapy following Endeavor zotarolimus-eluting stent implantation) trial22. MACCE at 12 months were non-inferior after six months vs. 12 months of DAPT (4.8% vs. 4.3%, p<0.001) in the EXCELLENT (Efficacy of XIENCE/Promus versus Cypher to rEduce Late Loss after stENTing) trial23. DAPT beyond 12 months was not more effective than aspirin alone in reducing the rate of MI and cardiac death in 2,701 patients treated with DES (HR 1.65, 95% CI: 0.80-3.36, p=0.17)24. In the PROlonging Dual antiplatelet treatment after Grading stent-induced Intimal hyperplasia studY (PRODIGY), patients receiving clopidogrel for six vs. 24 months had a similar rate of ischaemic events and stent thrombosis at two years17. Furthermore, in 3,119 patients treated with zotarolimus DES, the rates of death, MI, stroke and major bleeding at one year were similar with three months or 12 months of clopidogrel25. More recently, the SECURITY (Second Generation Drug-Eluting Stent Implantation Followed by Six-Versus Twelve-Months Dual Antiplatelet Therapy) trial26 and the ISAR-SAFE (Intracoronary Stenting and Antithrombotic Regimen: Safety And EFficacy of six months Dual Antiplatelet Therapy After drug-Eluting Stenting) trial27 reported similar rates of MACCE in patients with 12 months of DAPT compared to six months only (3.7% vs. 4.5%; difference 0.8%; 95% CI: -2.4-1.7; p=0.469, and 1.5% vs. 1.6%; HR 0.91, 95% CI: 0.55-1.50; pforsuperiority=0.70, respectively). Similarly, in the ITALIC plus (Is There A LIfe for DES after discontinuation of Clopidogrel) trial, the 2,031 patients treated with new-generation DES (XIENCE V®; Abbott Vascular, Santa Clara, CA, USA) had a similar rate of MACCE (death MI, stroke, TVR, major bleeding) whether they were treated with clopidogrel for six or 24 months (1.6% vs. 1.5%; HR 1.07, 95% CI: 0.52-2.22; p=0.85)28.

Registry data have shown increased one-year stent thrombosis rates after DAPT discontinuation within 30 days post PCI but not after one month (3.6% vs. 0.1%, log-rank p<0.001). DAPT interruption >1-12 months was provocatively associated with a lower rate of stent thrombosis compared to patients with no DAPT interruption within a year (0.1% vs. 0.8%, log-rank p<0.001)29. In a real-world registry, Mehran et al reported that thrombotic events after PCI largely occur while patients are still on DAPT, with an early risk of events due to disruption, irrespective of stent type (DES or BMS)20.

Finally, extending the duration of DAPT was not associated with a reduction in all-cause death (OR [95% CI] 1.15 [0.85-1.54], p=0.36), MI (OR 0.95 [0.66-1.36], p=0.77), stent thrombosis (OR 0.88 [0.43-1.81], p=0.73), or cerebrovascular events (OR 1.51 [0.92-2.47], p=0.10) in a meta-analysis including 8,231 patients18.

Recently, in the large Dual Antiplatelet Therapy (DAPT) study, patients treated with 30 months of DAPT exhibited a substantial reduction of stent thrombosis (0.4% vs. 1.4%; HR 0.29, 95% CI: 0.17-0.48; p<0.001) and MACCE (4.3% vs. 5.9%; HR 0.71, 95% CI: 0.59-0.85; p<0.001), associated with a higher all-cause mortality (2.0% vs. 1.5%; HR 1.36, 95% CI: 1.00 -1.85; p=0.05) and increased rates of severe or moderate bleedings (2.5% vs. 1.6%; HR 1.61, 95% CI: 1.21 to 2.16; p=0.001) compared to patients treated with only 12 months of thienopyridine30. However, only selected patients were included in the trial, since investigators randomised patients who had already safely completed twelve months of DAPT after DES implantation. This represents a significant selection bias and implies that the DAPT results are only applicable to a selected population with global low ischaemic as well as bleeding risks. In addition, a large number of the patients were treated with first-generation DES associated with known delayed vascular healing, pro-inflammatory polymer or limited antirestenotic effect. In subgroup analysis, the effect of prolonged DAPT on MACCE was not similar among the different DES subtypes (p for heterogeneity=0.048)30.

More recently, the ZEUS trial (Zotarolimus-eluting Endeavor Sprint Stent in Uncertain DES Candidates) used a different approach to tackle the issue of efficacy versus safety in patients at risk for bleeding and/or thrombosis. This trial tested a zotarolimus-eluting stent (ZES) with an ultra-fast drug-eluting profile, followed by a variable DAPT duration based on patient comorbidities. The study demonstrated that ZES combined with an abbreviated and tailored DAPT regimen resulted in a lower risk of one-year MACCE in these uncertain candidates for DES implantation31. Nevertheless, these ZES are associated with a less powerful inhibition of neointima hyperplasia compared with the latest generation, slower eluting DES31.

Altogether, the improved safety of new-generation DES and the lack of strong evidence supporting prolonged DAPT in the elderly population clearly support the need for a dedicated trial assessing the balance of efficacy and safety in patients ≥75 years old treated with PCI.

Methods

STUDY DESIGN

A total of 1,200 subjects will be enrolled in the SENIOR (SYNERGY II Everolimus elutiNg stent In patients Older than 75 years undergoing coronary Revascularisation associated with a short dual antiplatelet therapy) trial, a prospective, single-blind, randomised multicentre trial registered at www.clinicaltrials.gov Identifier: NCT02099617. The first patient was included on 25 May 2014.

OBJECTIVES

The primary objective of this superiority study is to assess the effectiveness and safety of new-generation DES (SYNERGY™ II; Boston Scientific), compared with BMS (Omega™ or Rebel; Boston Scientific), in patients ≥75 years old in preventing the composite endpoint of all-cause mortality, MI, stroke and ischaemia-driven TLR at one year.

The secondary objectives are to assess the safety of PCI with DES versus BMS with identical duration of DAPT with respect to the rate of definite and probable stent thrombosis (Academic Research Consortium definition) at one year32.

Additional secondary outcome measures include all-cause and cardiovascular mortality, MI (periprocedural, spontaneous, Q-wave and non-Q-wave)33, stroke (all, ischaemic, and haemorrhagic) and all revascularisations (ischaemia-driven and non-ischaemia-driven) at 12 and 24 months. In addition, bleeding complications type 2, 3, and 5 according to the Bleeding Academic Research Consortium34 will be evaluated at one year.

Quality of life will be measured at 30 days post-procedure and at six, 12 and 24 months, and economic evaluation including direct comparison of medical care costs will be calculated at 12 and 24 months. Final cost-effectiveness will be assessed by the incremental cost per quality-adjusted year of life at two years.

DEFINITIONS

All-cause mortality is defined as any cause of death from inclusion until latest follow-up. Acute MI is defined by the evidence of myocardial necrosis in a clinical setting consistent with acute myocardial ischaemia according to the third universal definition of myocardial infarction33. Stroke is defined as appearance of a new focal neurologic deficit, with symptoms lasting less or more than 24 hours. Confirmation of the diagnosis with computerised tomography or magnetic resonance imaging will be used to differentiate between haemorrhagic and ischaemic strokes. All reported focal neurologic deficits reported during the study will be adjudicated. Ischaemia-driven target lesion revascularisation (TLR) is defined as any TLR for myocardial ischaemia (clinical evaluation or non-invasive assessment) under optimal medical treatment. All clinical events reported as being part of the primary endpoint, bleeding complication, or stent thrombosis will be reviewed by a dedicated, independent, clinical endpoint committee, unaware of the patient's treatment group.

PATIENT POPULATION

The inclusion and exclusion criteria are summarised in Table 2. Recruitment flow is summarised in Figure 1. The steps in determining trial eligibility and obtaining informed consent are designed to mirror daily clinical practice closely in order to optimise recruitment. Consecutive subjects above 75 years of age in whom revascularisation by PCI of at least one coronary artery stenosis with visually assessed diameter stenosis ≥70% (≥50% in the left main) will be identified and screened for study eligibility. Subjects eligible for enrolment as per the general inclusion and exclusion criteria will be asked to sign an informed consent for the randomised trial.

INFORMED CONSENT

All subjects must provide informed consent in accordance with the local institutional review board (IRB)/ethics committee (EC), using an IRB/EC-approved informed consent form. Final eligibility for the trial will be confirmed based on the pre-intervention angiography. Local ethics committee approval was obtained on 16 April 2014 (Comité de Protection des Personnes Ile de France III: 2014-A00281-46).

RANDOMISATION

Randomisation is carried out through a web-based system available 24 hours per day, all year round, and maintained by a data coordinating centre (Cardiovascular European Research Center, CERC, Massy, France).

The choice of antiplatelet agent and duration of DAPT are stratified upfront and are required to be entered in the Interactive Web Response System (IWRS) at randomisation, to avoid inequality between the two groups based on an unblinded physician's decision. MEASUREMENTS Table 3 summarises the schedule of measurements at 24 hours, 30 days and 180 days post procedure and annually thereafter for the duration of the study. In addition, telephone interviews will be conducted semi-annually to control vital status and identify intervening MACCE since the last in-hospital visit. Quality of life and depression data will also be collected at six and 12 months in the hospital.

REVASCULARISATION PROCEDURE

The transradial approach is recommended in experienced centres. The choice of guiding catheters, guidewires, predilatation, atherectomy devices, post-dilatation, and intracoronary imaging system is left to the investigator's discretion. A final inflation using non-compliant balloons is recommended. The final objective is to obtain a <20% residual stenosis with a TIMI grade 3 distal flow without the loss of any side branch ≥2.0 mm in diameter. Only one type of stent is allowed in a patient during the index procedure, should he receive >1 stent. The randomisation process will determine which stent is allocated for any patient. In case of a staged procedure, PCI will be performed within a month after inclusion with the same study stent(s).

ANTITHROMBOTIC REGIMEN

Antithrombotic regimens in the cathlab, including unfractionated heparin, low molecular weight heparin and bivalirudin are left to the physician's discretion. DAPT duration will be one month after PCI for stable angina and silent ischaemia, and six months after PCI for acute coronary syndromes, irrespective of the type of stent. Aspirin will be given at a loading dose of 150-300 mg (orally) or 80-150 mg (intravenously) and at an oral maintenance dose of 75-100 mg daily, indefinitely. The P2Y12 inhibitors added to aspirin before or immediately after PCI could be either clopidogrel (600 mg loading dose and 75 mg/d), prasugrel (60 mg loading dose and 5 mg/d orally, half the maintenance dose given to <75-year-old patients) or ticagrelor (180 mg loading dose and 90 mg/bid orally). In case of a staged procedure, the duration of DAPT will be six months from the index procedure in patients with acute coronary syndrome at baseline or one month starting from the final PCI in patients with stable or silent ischaemia at baseline.

SAMPLE SIZE

The study is powered to test the superiority of DES with a relative 25% reduction in the primary endpoint compared to BMS. Assuming a primary endpoint event rate of 31% for BMS at one year (interpolated from the most contemporary and accurate references)14,15,16,17, a minimum time to follow-up of one year and a constant dropout rate yielding 15% lost to follow-up at one year, then a sample size population of 560 subjects per arm will provide 80% power to demonstrate superiority using a chi-square test (two-sided alpha=0.05) comparing the event rates at one year from the Kaplan-Meier curves. A total of 1,200 patients (600 in each arm) will be randomised. The sample size calculation was performed in SAS version 9.2 (SAS Institute, Cary, NC, USA) using 10,000 simulations. Results from individual or secondary endpoints will only be considered to be hypothesisgenerating.

QUALITY OF LIFE, AND DEPRESSION ANALYSIS

Quality of life will be assessed using the SF-12v235 and the EuroQol-5D36 self-administered questionnaires. These questionnaires have been validated in populations with coronary artery disease37. Quality-adjusted survival for each treatment group is estimated on the basis of observed clinical outcomes (survival) and country-specific utility weights. Depression state will be assessed with the short version of the Geriatric Depression Scale used extensively in the elderly38.

COST-EFFECTIVENESS ANALYSIS

Medical care costs for the initial hospitalisation and for the one-and two-year follow-up periods will be assessed by a combination of "bottom-up" and "top-down" methods using patient-level detailed resource utilisation from the CRF, and DRG-specific costs from the national hospital activity-based costing study.

CARDIAC CATHETERISATION LABORATORY COSTS

Detailed resource use will be recorded for each procedure, and the cost of each item estimated on the basis of the most recent hospital acquisition cost for the item. Costs of additional disposable equipment, overheads, and depreciation for the cardiac catheterisation laboratory will be estimated from the DRG-specific average cost per procedure39.

OTHER HOSPITAL COSTS

All other hospital costs will be determined by using the national cost schedules, which provide itemised DRG-specific costs on a yearly basis. Hospital costs will be determined by multiplying the per diem itemised hospital costs (excluding procedural costs) by the actual length of stay of each patient in the trial. The most recent cost study available will be used.

OTHER COSTS

Outpatient services will be assessed by patient self-report of medication and service utilisation, and their costs be estimated from the most recent national cost schedules.

OUTCOMES

Since the primary endpoint is a reduction in MACCE, the primary endpoint for the costeffectiveness analysis is the incremental cost per event avoided by DES compared with BMS. This disease-specific cost-effectiveness ratio will be calculated by dividing the difference in mean one-year and two-year medical care costs for the two treatment groups by the difference in event rates over the same time frame. Final cost-effectiveness will be assessed for cost per quality-adjusted year of life gained at two years.

STATISTICAL ANALYSIS

All primary analyses will be carried out using the intention-to-treat principle. The rates of the primary endpoint at one year in both groups will be determined from a Kaplan-Meier curve and compared by means of a chi-square test. In addition, a relative risk estimate with a 95% confidence interval will be provided. The rates of definite and probable stent thrombosis at one year will be analysed similarly. Cost data will be reported as both mean and median values and compared by t-tests. To estimate the uncertainty surrounding the cost-utility ratio, we will calculate bias-corrected CIs by the bootstrap method using 1,000 repeated samplings of the study population. All statistical analyses will be described in a statistical analysis plan, which will be finalised before the end of the study.

Limitations

The design of the SENIOR trial will only allow definite conclusions with regard to the primary combined endpoint, in view of the planned sample size. Given the expected relative scarcity of stent thrombosis and major bleeding complications, as well as all-cause mortality, dedicated trials in much larger populations of elderly patients will be needed to address the safety/benefit ratio of combining DES and short DAPT duration in these high-risk patients.

Conclusions

The SENIOR trial is designed to compare a new-generation DES with standard BMS in elderly patients receiving a similarly short duration of DAPT. A strategy combining the efficacy of this latest generation of DES to reduce ischaemia-driven revascularisations and re-hospitalisations with the safety of a short duration of DAPT could be of particular benefit in a high bleeding risk population such as the elderly.

Impact on daily practice

Improved outcomes associated with newer-generation stents without increased bleeding risk may alter the unfavourable risk/benefit ratio with first-generation DES and thus modify PCI strategies in elderly patients with coronary artery disease.

Figure 1 .

 1 Figure 1. SENIOR study design.

Acknowledgements

Clinical trial operational management of the study is performed by CERC.

Funding

The study is funded by an unrestricted educational grant through the Investigator Research Program, from Boston Scientific.

Conflict of interest statement

O. Varenne has received speaker fees from Boston Scientific and Abbott Vascular. T. Cuisset has received consulting or speaker fees from Abbott Vascular, AstraZeneca, Biotronik, Boston Scientific, Cordis, Daiichi Sankyo, Edwards, Eli Lilly, Hexacath, Iroko Cardio, Medtronic, Servier and Terumo. M. Sabaté has received consulting fees from Abbott Vascular. O. Hanon has received consulting or speaker fees from AstraZeneca, Bayer, Bristol-Myers Squibb, Boehringer, Boston Scientific, Novartis, Pfizer, Sanofi-Aventis, Servier, and Vifor. I. Durand-Zaleski has received consulting or speaker fees from AbbVie, Amgen, Sanofi, Janssen, BMS, Pfizer, and Medtronic. The other authors have no conflicts of interest to declare.


FAST AND ADAPTIVE BLIND AUDIO SOURCE SEPARATION USING RECURSIVE LEVENBERG-MARQUARDT SYNCHROSQUEEZING

Dominique Fourer Geoffroy Peeters

UMR STMS (IRCAM -CNRS -UPMC) dominique@fourer.fr, geoffroy.peeters@ircam.fr

This paper revisits the Degenerate Unmixing Estimation Technique (DUET) for blind audio separation of an arbitrary number of sources given two mixtures through a recursively computed and adaptive time-frequency representation. Recently, synchrosqueezing was introduced as a promising signal disentangling method which allows to compute reversible and sharpen time-frequency representations. Thus, it can be used to reduce overlaps between the sources in the time-frequency plane and to improve the sources' sparsity which is often exploited by source separation techniques. Furthermore, synchrosqueezing can also be extended using the Levenberg-Marquardt algorithm to allow a user to adjust the energy concentration of a time-frequency representation which can be efficiently implemented without the FFT algorithm. Hence, we show that our approach can improve the quality of the source separation process while remaining suitable for real-time applications.

Index Termsblind source separation, time-frequency analysis, synchrosqueezing, Levenberg-Marquardt algorithm.

INTRODUCTION

Source separation is the task which aims at estimating the source components present in a mixture [START_REF] Comon | Handbook of Blind Source Separation: Independent component analysis and applications[END_REF]. It could allow a user to freely manipulate each isolated instrument in a polyphonic audio mixture and could find many other practical applications (e.g. karaoke, remixing, denoising, etc.). The blind degenerate case (where the number of sources is greater than the number of observed mixtures) remains the most challenging. State-of-the-art methods should use strong assumptions over the sources, such as sparsity [START_REF] Chenot | Robust sparse blind source separation[END_REF], harmonicity [START_REF] Duan | Unsupervised single-channel music source separation by average harmonic structure modeling[END_REF], or disjoint orthogonality [START_REF] Jourjine | Blind separation of disjoint orthogonal signals: Demixing N sources from 2 mixtures[END_REF] which can only be revealed thanks to a proper signal representation. Nowadays, these signal properties are also exploited by promising recent methods based on deep neural networks [START_REF] Nugraha | Multichannel audio source separation with deep neural networks[END_REF] or Kernel Additive Modeling (KAM) [START_REF] Liutkus | Kernel additive models for source separation[END_REF] which have shown their ability to capture source-specific features from a time-frequency representation (TFR).

The synchrosqueezing transform [START_REF] Daubechies | A nonlinear squeezing of the continuous wavelet transform[END_REF][START_REF] Auger | TF reassignment and synchrosqueezing: An overview[END_REF] was introduced as a sharpening method which contrarily to the reassignment [START_REF] Auger | Improving the readability of time-frequency and time-scale representations by the reassignment method[END_REF], provides reversible TFRs. This method was recently extended to frequency modulated signals [START_REF] Oberlin | Second-order synchrosqueezing transform or invertible reassignment? Towards ideal time-frequency representations[END_REF][START_REF] Fourer | Chirp rate and instantaneous frequency estimation: Application to recursive vertical synchrosqueezing[END_REF] and was com- bined with the Levenberg-Marquardt algorithm [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF] to become adaptive thanks to a damping parameter. These methods have shown their interest for disentangling multicomponent signals or to obtain physically interpretable components [START_REF] Fourer | The ASTRES toolbox for mode extraction of non-stationary multicomponent signals[END_REF].

Thus, we propose to revisit a well known and efficient algorithm for blind source separation called Degenerate Unmixing Estimation Technique (DUET) [START_REF] Jourjine | Blind separation of disjoint orthogonal signals: Demixing N sources from 2 mixtures[END_REF][START_REF] Rickard | Blind Speech Separation, chapter The DUET blind source separation algorithm[END_REF], which operates in the time-frequency plane using a disjoint orthogonality assumption between the sources. This approach can estimate an arbitrary number of sources from a stereophonic mixtures in a blind configuration and has shown its efficiency on realworld audio signals. Due to its simplicity and its robustness, the DUET algorithm is suitable for an investigation of the TFR role in a source separation algorithm in realistic blind audio source separation scenarios. We also show that our proposed approaches can be implemented in terms of recursive filtering to allow real-time applications without using the Fast Fourier Transform (FFT) algorithm.

The paper is organized as follows. The Levenberg-Marquardt algorithm applied to the recursive synchrosqueezed Short-Time Fourier Transforms (STFT) is introduced in Section 2. A blind source separation method which combines DUET and synchrosqueezing is then proposed in Section 3 and evaluated by numerical experiments in Section 4. Finally, results and future works are discussed in Section 5.

THE RECURSIVE LEVENBERG-MARQUARDT SYNCHROSQUEEZING TRANSFORM

Let X h (t, ω) denote for any time t and any angular frequency ω, the STFT of a signal x(t) using a differentiable analysis window h(t), defined as:

X h (t, ω) = R x(u)h(t -u) * e -jωu du (1) = e -jωt R x(t -u) h(u) * e jωu g(u,ω) du (2)
z * being the complex conjugate of z and j 2 = -1. Since |X h (t, ω)| 2 provides a TFR called spectrogram, a signal reconstruction can be provided using [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF]:

x(t -t 0 ) = 1 h(t 0 ) * R X h (t, ω) e jω(t-t0) dω 2π (3)
for any time delay t 0 ≥ 0 verifying h(t 0 ) = 0. In [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF][START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned scalogram and of the synchrosqueezed wavelet transform[END_REF], we showed that Eq. ( 2) can be viewed as a convolution product of x with a filter g(t, ω) = h(t) e jωt , which can be efficiently implemented in terms of a recursive filtering process if we use a specific analysis window h k (t) = t k-1 T k (k-1)! e -t T U (t), with k ≥ 1 the filter order, T the time spread of the window and U (t) the Heaviside step function. Computation details and a Matlab implementation of this approach is freely available as a part of ASTRES toolbox in [START_REF] Fourer | The ASTRES toolbox for mode extraction of non-stationary multicomponent signals[END_REF].

Synchrosqueezed STFT

Synchrosqueezing is a post-processing technique which enhances the time-frequency localization of a transform while allowing signal reconstruction. For the STFT, the synchrosqueezing transform is based on the synthesis formula given by Eq. ( 3) which leads to the following definition [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF]:

SX h (t,ω) = R X h (t, ω ) e jω (t-t0) δ(ω -ωx (t,ω )) dω (4)
where δ(t) denotes the Dirac distribution. This transform provides a sharpened TFR computed as |SX h (t, ω)| 2 (cf. illustration in Fig. 1), when an efficient local Instantaneous Frequency Estimator (IFE) is used for ωx [START_REF] Fourer | Chirp rate and instantaneous frequency estimation: Application to recursive vertical synchrosqueezing[END_REF]. Usually, the frequency reassignment operator is used such as [START_REF] Auger | Improving the readability of time-frequency and time-scale representations by the reassignment method[END_REF]:

ωx (t, ω) = ω + Im X Dh (t, ω) X h (t, ω) , with Dh(t) = dh dt (t).
(5) An enhanced second-order IFE could also be used to compute the vertical synchrosqueezed STFT as in [START_REF] Fourer | Chirp rate and instantaneous frequency estimation: Application to recursive vertical synchrosqueezing[END_REF]. Thus, the original signal x can be recovered from the synchrosqueezed STFT using the following reconstruction formula [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF]:

x(t -t 0 ) = 1 h(t 0 ) * R SX h (t, ω) dω 2π (6)
where the integration interval can profitably be restricted to the vicinity of the signal ridge for components extraction.

Levenberg-Marquardt synchrosqueezing

Reflection on synchrosqueezing was continued, and by analogy, the Levenberg-Marquardt root finding algorithm has been used to compute new reassignment operators to adjust the energy localization in the time-frequency plane through a damping parameter µ [START_REF] Auger | Making reassignment adjustable: the Levenberg-Marquardt approach[END_REF]. This parameter could be locally matched to the signal content by a voice activity detector [START_REF] Jo | Statistical model-based voice activity detection using support vector machine[END_REF] or by a noise only/signal+noise binary detector [START_REF] Jo | Statistical model-based voice activity detection using support vector machine[END_REF][START_REF] Huillery | On the description of spectrogram probabilities with a chi-squared law[END_REF]. The new operators are computed as:

tµ (t, ω) ωµ (t, ω) = t ω -∇ t R h x (t, ω) + µI 2 -1 R h x (t, ω) (7)
with

R h x (t, ω) = t -tx (t, ω) ω -ωx (t, ω) (8)
∇ t R h x (t, ω) = ∂R h x ∂t (t, ω) ∂R h x ∂ω (t, ω) (9)
I 2 being the 2 × 2 identity matrix and tx being the time reassignment operator computed as:

tx (t, ω) = t -Re X T h (t, ω) X h (t, ω) , with T h(t) = t h(t).
(10) Thus, the Levenberg-Marquardt synchrosqueezing transform can be computed by replacing ω in Eq. ( 4) by ωµ . This leads to new adaptive and reversible TFRs which can also be efficiently computed through recursive filtering [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF][START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned scalogram and of the synchrosqueezed wavelet transform[END_REF].

BLIND SOURCE SEPARATION

Now, let's consider a two-channel mixture made of I ≥ 2 sources s i . Each active source in the first channel x 1 , is attenuated by a factor a i and delayed by a duration τ i (expressed in seconds), in the second channel x 2 . Thus, the resulting mixture can be modeled as:

x 1 (t) = I i=1 s i (t) x 2 (t) = I i=1 a i s i (t -τ i ) ( 11
)
which can be expressed in the time-frequency domain as:

X h 1 (t,ω) X h 2 (t,ω) = 1 . . . 1 a 1 e -jωτ1 . . . a I e -jωτ I    S h 1 (t, ω) . . . S h I (t, ω)    .
(12) Hence, our proposal consists in replacing the computed STFTs S i by the desired TFR (i.e. a synchrosqueezed version) in the whole proposed source separation algorithm.

Mixing parameters estimation

DUET algorithm [START_REF] Jourjine | Blind separation of disjoint orthogonal signals: Demixing N sources from 2 mixtures[END_REF][START_REF] Rickard | Blind Speech Separation, chapter The DUET blind source separation algorithm[END_REF] can recover both the mixing parameters and estimates of the original sources by assuming that only one source is active at each time-frequency coordinate (t, ω). This allows us to write the following expressions when a source i is active at a given (t, ω) coordinate:

X h 1 (t,ω) X h 2 (t,ω) = 1 a i e -jωτi S h i (t, ω). (13)
Thus, the mixing parameters can be estimated when X 1 (t, ω) = 0 (resp. X 2 (t, ω) = 0) such as:

âi (t, ω) = X h 2 (t, ω) X h 1 (t, ω) (14)
τi (t, ω) = - 1 ω arg X h 2 (t, ω) X h 1 (t, ω) , ∀ω = 0. ( 15
)
For the sake of enhancing the robustness, DUET algorithm computes a smoothed 2D histogram using the symmetric attenuation instead of â, computed as:

αi (t, ω) = âi (t, ω) - 1 âi (t, ω) (16)
The signal energy is then distributed according to the estimates α and τ over the corresponding axes with a resolution ∆ α and ∆ τ . Hence, the histogram is computed as:

H(α, τ ) = (t,ω)∈I(α,τ ) |X h 1 (t, ω)X h 2 (t, ω)| 2 dtdω (17)
with:

I(α, τ ) = {(t, ω) : |α -α(t,ω)| < ∆ α , |τ -τ (t,ω)| < ∆ τ }
The parameters associated to each source can be deduced from the prominent detected peaks in H(α, τ ) for which the mixing parameter âi can be recovered from αi using:

âi = αi + α2 i + 4 2 (18)
which can be deduced after inverting Eq. ( 16).

Sources estimation

Each time-frequency coordinate associated to the histogram given by Eq. ( 17) can be associated to the prominent source using its corresponding mixing parameters such as:

J(t, ω) = arg min k âk e -jω τk X h 1 (t, ω) -X h 2 (t, ω) 1 + â2 k (19)
which allows the computation of the binary separation mask M i of each source computed as:

M i (t, ω) = 1 if J(t, ω) = i 0 otherwise . ( 20
)
Finally, the TFR of each source is simply recovered by:

Ŝi (t, ω) = M i X h 1 (t, ω) + âk e +jω τk X h 2 (t, ω) 1 + â2 k (21)
for which the waveform is reconstructed using the corresponding synthesis formula (i.e. Eq. ( 3) when STFT is used or Eq. ( 6) for the synchrosqueezed STFT).

NUMERICAL EXPERIMENTS

Audio dataset

Our experiments use the Bach10 dataset 1 which contains 10 musical excerpts of classical music for which the isolated tracks are availables. Each musical piece is made of 4 sources (string instruments) resampled at F s = 8000 Hz and truncated at the 5 first seconds. The simulated stereophonic mixtures are computed using random mixing parameters a i ∈ {0.4, 0.6, 0.8, 1} and τ i ∈ [-2

Fs ; + 2 Fs ] ensuring that all of the original sources have distinct parameters.

TFR and W-disjoint orthogonality

Two sources s 1 , s 2 are said window-disjoint orthogonal if their windowed Fourier transforms (or STFTs) verify [START_REF] Rickard | On the approximate W-disjoint orthogonality of speech[END_REF]:

S h 1 (t, ω)S h 2 (t, ω) = 0 ∀(t, ω). (22)
We now propose to extend this definition to any TFR since the source separation quality of DUET depends on how the sources can overlap in the time-frequency plane. In [START_REF] Rickard | Blind Speech Separation, chapter The DUET blind source separation algorithm[END_REF], the author proposes to measure the W-disjoint orthogonality of a source i in a mixture, for a given separation mask M i using: A high value for D i corresponds to a better expected source separation quality provided by DUET. Thus, a comparison of the averaged W-disjoint orthogonality measured using Eq. ( 3) for each TFR computed on the Bach10 dataset, is displayed in Fig. 3. Here, D i of all the sources is also averaged between all the pieces of the dataset. Each TFR is computed using M = 1024 discrete frequency bins. A classical STFT computed using FFT with a Hann window of length 128 ms (1024 samples at F s = 8000 Hz) with an 1 2 -overlap between adjacent frames is used as a baseline method. For the recursively computed TFRs, an Infinite Impulse Response (IIR) filter of order k = 5 using a window time spread equal to L = T F s = 100 is used. For the reconstruction a delay equal to n 0 = (k -1)L samples, which corresponds to the maximum of the causal window, is considered (cf. [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF] for details). Our results show that the synchrosqueezed STFT provides a better W-disjoint orthogonality than the STFT (recursive or classical). When combined with the Levenberg-Marquardt algorithm, a maximal D i is reached with µ = 0.06. As theoretically investigated in [START_REF] Auger | Making reassignment adjustable: the Levenberg-Marquardt approach[END_REF][START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF], a lower value of µ improves the time-frequency energy localization and converges to the recursive synchrosqueezed STFT results and higher values for µ converge to the recursive STFT results due to a poorer time-frequency localization. Interestingly, the best results are provided by a trade-off with a value of µ which is not too small. The validity of this choice is also confirmed by the source separation results presented in the next section.

D i (M i ) = R 2 |M i (t,ω)S h i (t,ω)| 2 dtdω - R 2 |M i (t,ω)Y i (t,ω)| 2 dtdω R 2 |S h i (t,ω)| 2 dtdω (23) where Y i (t, ω) = ∀j =i S h j (t,

Blind source separation results

Now, we compare the source separation results provided by the proposed methods using the same configuration as in Section 4.2, which are applied to the Bach10 dataset. For each compared method, the mixing parameters are assumed to be known and identical The source separation quality is measured in terms of Reconstruction Quality Factor (RQF) computed as [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF]: RQF = 10 log 10

n |x[n]| 2 n |x[n]-x[n]| 2
and in terms of Signal-to-Interference Ratio (SIR), Signal-to-Distortion Ratio (SDR) and Signal-to-Artifact Ratio (SAR) which are commonly used measures computed through BSS Eval2 [START_REF] Vincent | Performance measurement in blind audio source separation[END_REF]. According to the results displayed in Fig. 2, best separation results (in particular with a higher SIR) are reached using the recursive Levenberg-Marquardt synchrosqueezed STFT using µ = 0.06. This result confirm the expectation provided by the W-disjoint orthogonality in Fig. 3. As also expected, the recursive synchrosqueezed STFT outperforms the STFT. However, the recursive version of the STFT obtains slightly better results than the STFT computed using the FFT, despite a lower averaged value of D i . For the comparison, Fig. 2(b) displays results for µ = 10 and shows that Levenberg-Marquardt synchrosqueezing obtains results comparable to those provided by STFT when µ is too high.

CONCLUSION

In this paper, we have proposed new extensions of the DUET source separation algorithm using a recursive implementation of the Levenberg-Marquardt synchrosqueezed STFT. We have shown that synchrosqueezing allows to compute a sharpen and reversible TFR which can improve the disjoint orthogonality between the sources. This results in a significant improvement of the source separation results in comparison with classical TFRs (∆SIR≈+5dB in average). Future works will consist in investigating new source separation methods based on TFR masking using the synchrosqueezing technique.

2 Fig. 1 .

 21 Fig. 1. Comparison of the TFRs provided by the recursively computed spectrogram (a) and the squared modulus of the recursive synchrosqueezed STFT (b). The analysed signal is a mixture made of 4 audio sources from the Bach10 dataset.

Fig. 3 .

 3 Fig. 3. Approximated W-disjoint orthogonality using different TFRs, as a function of µ. Results are averaged over 10 mixtures made of 4 sources from the Bach10 dataset.

1Fig. 2 .

 2 Fig. 2. Comparison of the source separation results provided by the proposed methods applied on the Bach10 dataset. (a) and (b) use different values of the damping parameter µ used by the recursive Levenberg-Marquardt synchrosqueezed STFT (other TFRs are not affected by µ).

BSS Eval: http://bass-db.gforge.inria.fr/bss_ eval/