Alexandr Oshchepkov

Antoine Bonnefont

Gaël Maranzana

Elena R Savinova

Marian Chatenet
email: marian.chatenet@grenoble-inp.fr

Direct borohydride fuel cells: a selected review of their reaction mechanisms, electrocatalysts and influence of operating parameters on their performance

Keywords: Borohydride Oxidation Reaction, Direct Borohydride Fuel Cells, Platinum, Nickel, Palladium, Hydrogen escape Highlights

Direct borohydride fuel cells (DBFC) oxidize an easily-stored energy-dense borohydride fuel (sodium borohydride: NaBH4), that in theory reacts ca. 400 mV below H2 and produce 8 electrons per BH4 -anion. However, the borohydride oxidation reaction (BOR) does not fully meet these promises in practice: the electrocatalyst nature, structure and state-of-surface, and the operating conditions (pH, BH4 -concentration, temperature, fluxes) noticeably influence the BOR kinetics and mechanism. Nickel and platinum-based catalysts both have assets for the BOR. DBFCs can only yield decent performance if their separator combines high ionconductivity and efficient separation of the reactants; cation-exchange membranes, anionexchange membranes, bipolar membranes and porous separators all have their own advantages and drawbacks. Besides the anode, the choice of separator must consider the DBFC cathode reaction, where oxygen (air) or hydrogen peroxide are reduced, provided adapted catalysts are used. All these aspects drive the DBFC performance and stability/durability.

Introduction

Direct borohydride fuel cells (DBFC) increasingly stimulate the scientific community since two decades, following the pioneering work of Amendola et al. [START_REF] Amendola | A novel high power density borohydride-air cell[END_REF]. DBFCs oxidize a borohydride fuel (e.g. sodium borohydride: NaBH4) at their anode [START_REF] Indig | Sodium Borohydride, an Interesting Anodic Fuel .1[END_REF], fed as alkaline anolyte (BH4 -is only stable at high pH [START_REF] Mochalov | A generalized scheme for hydrolysis of borohydride ion and diborane[END_REF]). The borohydride oxidation reaction (BOR, Eq.1) produces 8 electrons per BH4 -anion in theory, and its equilibrium potential (-0.41 V vs RHE) is 400 mV below the equilibrium potential of the hydrogen electrode, the latter being the anode in H2-fed fuel cells [START_REF] Olu | Evaluation of anode (electro)catalytic materials for the direct borohydride fuel cell: Methods and benchmarks[END_REF]. This grants DBFC high theoretical energy-density and explains their interest to power portable electronic or small mobility devices. However, this low theoretical operating potential induces drawbacks: depending on the anode electrocatalyst, the BOR may compete with the electrochemical hydrogen evolution (HER) and hydrogen oxidation (HOR) reactions, and with the heterogeneous borohydride hydrolysis. Hence, proper anode catalyst and structure must be selected for a DBFC anode; Section 2 summarizes recent achievements on the theme, by focusing in particular on catalysts for which recent progresses in the understanding of the reaction mechanism were made. To efficiently separate DBFC reactants, an operating cell shall employ a properly-designed separator (Section 3), but also a dedicated cathode catalyst; the choice of these materials must be adapted to the cathode reaction: (gaseous) oxygen reduction reaction, ORR, in a classical DBFC (Eq.2), or (acidic liquid) hydrogen peroxide reduction reaction, HPRR, in a so-called H2O2-DBFC (Eq.3) (Section 4). In complete DBFCs, the interplay between these components and their morphology, structure and assembly is critical to the overall cell performance (Section 5). BH4 -+ 8 OH -→ B(OH)4 -+ 4 H2O + 8 e - (Eq.1)

BOR, E 0 = -0.41 V vs RHE, pH 14 = -1.24 V vs SHE O2 + 2 H2O + 4 e -→ 4 OH - (Eq.2)

ORR, E 0 = 1.23 V vs RHE, pH 14 = 0.401 V vs SHE H2O2 + 2 H + + 2 e -→ 2 H2O (Eq.3)

HPRR, E 0 = 2.60 V vs RHE, pH 0 = 1.77 V vs SHE Several papers have already reviewed the DBFC operation and various components of the system [START_REF] Olu | Evaluation of anode (electro)catalytic materials for the direct borohydride fuel cell: Methods and benchmarks[END_REF][START_REF] Merino-Jiménez | Developments in direct borohydride fuel cells and remaining challenges[END_REF][START_REF] Olu | Anode Electrocatalysts for Direct Borohydride and Direct Ammonia Borane Fuel Cells[END_REF]. Here, special attention is devoted to recent papers mainly dealing with the BOR electrocatalysts and their reaction mechanisms, as well as the influence of cathode electrocatalysts, separators and operating parameters on the DBFC performance. an electrode passivated after applying potentials exceeding 0.5 V vs RHE [START_REF] Oshchepkov | Recent Advances in the Understanding of Nickel-Based Catalysts for the Oxidation of Hydrogen-Containing Fuels in Alkaline Media[END_REF] (denoted as NiOx/C in Figure 1B), becomes inactive towards low-potential BOR and catalytically-active only above ca. reproduced from [9] with permission from the American Chemical Society. (D) Review of RDE characterization of BOR for carbon-supported nanoparticles; replotted from [START_REF] Olu | Influence of the concentration of borohydride towards hydrogen production and escape for borohydride oxidation reaction on Pt and Au electrodesexperimental and modelling insights[END_REF] with permission from Elsiever. Data were taken from Simoes et al. [START_REF] Simões | Proc. ECS Trans[END_REF], Yi et al. [START_REF] Yi | Enhanced activity of Au-Fe/C anodic electrocatalyst for direct borohydride-hydrogen peroxide fuel cell[END_REF], Geng et al.

[13], and Oshchepkov et al. [9]. (E) number of electrons valorized during the BOR, recalculated from DEMS measurements; replotted from [START_REF] Pasqualeti | Borohydride electrooxidation on carbon-supported noble metal nanoparticles: Insights into hydrogen and hydroxyborane formation[END_REF] with permission from the American Chemical Society. (F) Hydrogen escape measured in a DBFC configuration and plotted against the current density; reproduced from [START_REF] Olu | Influence of the concentration of borohydride towards hydrogen production and escape for borohydride oxidation reaction on Pt and Au electrodesexperimental and modelling insights[END_REF] with permission from Elsevier. Data were taken from Boyacı San et al. [START_REF] Boyaci San | Evaluation of operating conditions on DBFC (direct borohydride fuel cell) performance with PtRu anode catalyst by response surface method[END_REF], Li et al. [START_REF] Li | Porous Carbon as Anode Catalyst Support to Improve Borohydride Utilization in a Direct Borohydride Fuel Cell[END_REF][START_REF] Li | Depression of hydrogen evolution during operation of a direct borohydride fuel cell[END_REF], Geng et al. [START_REF] Geng | Borohydride electrochemical oxidation on carbonsupported Pt-modified Au nanoparticles[END_REF][START_REF] Geng | Ni-Pt/C as anode electrocatalyst for a direct borohydride fuel cell[END_REF], Jamard et al. [START_REF] Jamard | Study of fuel efficiency in a direct borohydride fuel cell[END_REF][START_REF] Jamard | Life time test in direct borohydride fuel cell system[END_REF] and Park et al. [START_REF] Park | Influence of anode diffusion layer properties on performance of direct borohydride fuel cell[END_REF].

The OCP value varies as: Ni/C < Pd/C < Pt/C < Au/C and below 0 V vs RHE is determined by competition between the HER (Eq.4, negative currents) and the BOR (Eq.1, positive currents) (Figure 1).

2 H2O + 2 e -→ H2 + 2 OH - (Eq.4)

The heterogeneous hydrolysis of BH4 -(Eq.5) catalyzed by Pt, Pd and Ni can be seen as a sum of the cathodic HER (Eq.4) and the anodic BOR (Eq.1):

BH4 -+ 4 H2O → B(OH)4 -+ 4 H2 (Eq.5)

Eq.4 and Eq.5 contribute (with other processes) to hydrogen generation during the BOR (Section 2.2).

Hydrogen generation during the BOR

Hydrogen generation during the BOR is evaluated in half-cell and in full DBFC by in situ DEMS measurements, or using a PEMFC module at the DBFC outlet, respectively. While Eq.4

accounts for hydrogen generation (from water) below 0 V vs RHE, H2 is also detected at positive potentials and high current densities. DEMS studies using deuterated fuel [START_REF] Jusys | Borohydride electrooxidation over Pt/C, AuPt/C and Au/C catalysts: Partial reaction pathways and mixed potential formation[END_REF] on Pt and Au show that high-potential H2 is generated from BD4 -when the electrode surface is poisoned either by surface oxides (at high anodic potentials, Figure 1E) or by BHx intermediates (at high borohydride concentration and/or low ECSA) [START_REF] Olu | Influence of the concentration of borohydride towards hydrogen production and escape for borohydride oxidation reaction on Pt and Au electrodesexperimental and modelling insights[END_REF]. High-potential H2 generation on Pt and Au may follow the occurrence of some dissociation steps involving BH4 -or reaction intermediates, e.g. BHx,ad (Section 2.4). Figure 1F represents the hydrogen escape rate versus current density in DBFC configuration: H2 formation during the BOR results in decreased faradaic efficiency and number-of-transferred-electrons per BH4 -species from theoretical 8 down to 6 or even 2e - , depending on the catalyst and applied conditions (BH4 -concentration, potential, temperature, ECSA, surface coverage, etc.). While on Pt and Au the maximum number-of-transferredelectrons, approaches 8 under favorable conditions (Figure 1E), it does not exceed 4 on metallic Ni [START_REF] Oshchepkov | Insights into the borohydride electrooxidation reaction on metallic nickel from operando FTIRS, on-line DEMS and DFT[END_REF], probably because of its low HOR activity. Besides its impact on the faradaic efficiency, the released hydrogen may cause some problems during DBFC operation.

Influence of the concentration of borohydride

Figure 2 shows how the BH4 -concentration affects the BOR kinetics on bulk Pt, Pd, Au and Ni surfaces measured in RDE configuration: increased BH4 -concentration negatively shifts the OCP, because the BOR kinetics increases compared to the HER (Figure 2A). The lowest OCP values are observed for the metallic Ni electrode, because of its very low HER activity.

However, increased BH4 -concentration also favors larger surface-poisoning by stronglyadsorbed intermediate BHx,ad species, which depend on the ratio between the BH4 -species concentration in the electrolyte and the number of available surface sites (ECSA) for the BH4 - adsorption and reaction on the electrode. Figure 2B shows the influence of the BH4 - concentration on the BOR on Pt, Au and Pd: the drastic poisoning of the Pt electrode surface manifests itself in ca. 0.5 V shift of the BOR current wave towards positive potentials, resulting from the electrode surface blocking by strongly-adsorbed intermediate BHx,ad species [START_REF] Braesch | Borohydride oxidation reaction mechanisms and poisoning effects on Au, Pt and Pd bulk electrodes: From model (low) to direct borohydride fuel cell operating (high) concentrations[END_REF]. The effect is less pronounced for Pd and, especially, for Au electrodes (Figure 2B). An appropriate ratio between the concentration of OH -and BH4 -should also be maintained to achieve high BOR faradaic efficiency. According to Eq.1, this ratio should exceed 8, otherwise, problems related to local pH decrease in the vicinity of the electrode surface may appear [START_REF] Oshchepkov | Insights into the borohydride electrooxidation reaction on metallic nickel from operando FTIRS, on-line DEMS and DFT[END_REF], facilitating undesirable BH4 -hydrolysis [START_REF] Mochalov | A generalized scheme for hydrolysis of borohydride ion and diborane[END_REF].

Stable BOR activity is also mandatory for practical applications. Close to 0 V vs RHE, noble metals suffer from severe surface poisoning, resulting in prompt decay of the BOR activity at 0.2 V vs RHE (Pt/C and Pd/C, Figure 2C), which is accelerated with increased BH4 - concentration from 5 to 50 mmol L -12 . In opposition, metallic Ni/C yields relatively stable BOR activity, revealing the absence of strong poisoning under relevant BOR operation: the affinity of Ni to oxygen species (like OH -) at relatively low potentials facilitates complete oxidation of the BOR intermediates, as revealed by in situ FTIR measurements [START_REF] Oshchepkov | Insights into the borohydride electrooxidation reaction on metallic nickel from operando FTIRS, on-line DEMS and DFT[END_REF]. which have been calculated by DFT (Table 1). On Pt, BH4 -adsorbs dissociatively, forming strongly-adsorbed BHad and Had. The latter species are easily oxidized on Pt above 0 V vs RHE (contributing to the currents), but escape as H2 below 0 V vs RHE (hence H2 detection in DEMS). To account for the 'high-potential' H2 escape, an incomplete BH4 -dissociation into BH3,ads, was proposed, the latter occurring on Pt 'poisoned' either by surface oxides or by BHx intermediates (Figure 2D). Figure 2E shows Pt surface-coverage with BH3,ads and BHads intermediates at different borohydride concentrations. BH3,ads can desorb from the "poisoned"

Pt surface to form BH3OH -, which can be detected using a RRDE. In contrast, the low BH4,ads binding-energy on Au surface results in slow BOR kinetics around 0 V vs RHE, requiring significant overpotential (ca. 0.7 V) to initiate the reaction. 3 Several types of separator/membranes for the DBFC This section briefly compares various types of DBFC separators focusing on the advantages and drawbacks of either choice rather than a comprehensive analysis of currently existing materials.

Cation Exchange membranes (CEM)

CEM, the most advanced on an industrial/commercial viewpoint, possess numerous advantages: high chemical stability, mechanical properties and commercial availability. In theory, CEMs exhibit reduced fuel cross-over (Donnan exclusion of BH4 -anion from SO3 - groups), but cannot suppress it, which can compromise the cathode performance if its catalyst is not BH4 --tolerant (Section 4) [START_REF] Liu | Influences of fuel crossover on cathode performance in a micro borohydride fuel cell[END_REF]. In a DBFC, a CEM operates in Na + form (for NaOH-based anolytes), which compromises the cell Ohmic-drop, owing to the low conductivity of Na + -CEMs versus H + -CEMs. Besides, this enables NaOH displacement towards the cathode side, where (for O2-fed DBFCs) it tends to precipitate, leading to reduced O2 mass-transport efficiency to the cathode sites [START_REF] Ould-Amara | Operating heterogeneities within a direct borohydride fuel cell[END_REF] (Figure 3A), hence depreciating the cathode and DBFC performance. For H2O2-DBFCs, CEMs lead to intense proton migration/diffusion from the (acidic) catholyte side to the anode side [START_REF] Stroman | A calibrated hydrogenperoxide direct-borohydride fuel cell model[END_REF], promoting severe BH4 -hydrolysis and depreciated performance (the cell anode then behaves like in a standard hydrogen fuel cell) [START_REF] Wang | Efficient pH-gradientenabled microscale bipolar interfaces in direct borohydride fuel cells[END_REF]. and its oxidation products (NaBO2) can be deposited in the channels of the cathode bipolar plate; reproduced from [START_REF] Jamard | Life time test in direct borohydride fuel cell system[END_REF] with permission from Elsevier. (C) Illustration of the way a H2O2-DBFC operates with pH-gradient-enabled microscale bipolar interface (BPM). Reproduced from [34] with permission from the American Chemical Society.

Anion-Exchange membranes (AEM)

AEM should prevent such NaOH (DBFCs) or H + (H2O2-DBFCs) displacement. AEM enabled the best-reported performance for DBFCs: 810 mW cm -2 , for a 5 cm² cell operated at 70°C, with a Pd+Ni-based anode (5 wt.% NaBH4 in 10 wt.% NaOH anolyte) and a Pt/C cathode (O2)

[35]. Many home-made (and then commercial) AEM were then tested in DBFC; their main drawback is associated to the unavoidable BH4 -(fuel) and BO2 -(final product) anion crossover they generate [START_REF] Jamard | Life time test in direct borohydride fuel cell system[END_REF], which leads to the re-precipitation of these compounds in the cathode and in its bipolar plate channels (Figure 3B). The corresponding non-negligible presence of fuel at the cathode renders mandatory the use of either BH4 --tolerant ORR catalysts or complex balance-of-plant to avoid detrimental mixed potential at the cathode and reach high performance. It is wise to say that non-noble cathode materials have assets in terms of fuel tolerance, and that they have a chance to be stable when used at the interface of an AEM, thus allowing DBFC to operate without noble metal catalysts (Section 4).

Bipolar membranes (BPM)

BPMs, combining a CEM side and an AEM side, are relevant for liquid-liquid DBFCs (H2O2-DBFCs), where they enable to maintain the required pH-gradient between the alkaline BH4 - anolyte and acidic H2O2 catholyte [START_REF] Wang | Efficient pH-gradientenabled microscale bipolar interfaces in direct borohydride fuel cells[END_REF][START_REF] Chatenet | Tailoring membranes[END_REF] (Figure 3C). Proper BPM operation requires that water-splitting easily occurs at the CEM|AEM interface, which implies an unavoidable junction potential [START_REF] Chatenet | Tailoring membranes[END_REF]; the OH -and H + produced then travel to the anode and cathode sides of the cell, respectively, to participate in the BOR and HPRR. BPM can lead to high-performance H2O2-DBFC [START_REF] Wang | Efficient pH-gradientenabled microscale bipolar interfaces in direct borohydride fuel cells[END_REF], but involve non-negligible consumption of base from the anolyte and acid from the catholyte, which limits the cell practical energy-density [START_REF] Chatenet | Tailoring membranes[END_REF]. The interest of BPM has not yet been demonstrated for classical (O2-fed) DBFCs.

Porous separators (or membraneless cells)

Membraneless DBFCs were reported, either in conventional DBFC operation with a cobaltbased anode and LaNiO3 (or MnO2) fuel-tolerant cathodes [START_REF] Yang | A direct borohydride fuel cell with a polymer fiber membrane and non-noble metal catalysts[END_REF][START_REF] Ma | Effect of cobalt precursors on Co3O4 anodic catalyst for a membrane-free direct borohydride fuel cell[END_REF], or with a ceriumammonium-nitrate reduction at the cathode [START_REF] Mota | Membraneless, Room-Temperature, Direct Borohydride/Cerium Fuel Cell with Power Density of Over 0.25 W/cm(2[END_REF]. This latter strategy is poorly compatible with high cell performance and easy operation, owing to complex fuel/oxidant management when the anode and cathode are not really separated. Porous separators have nevertheless been successfully employed in "Swiss-roll" mixed reactant cells, in which (in-principle) fuel-tolerant ORR catalyst (e.g. MnO2) and oxidant-tolerant BOR catalyst must be used [START_REF] Serov | Borohydride-tolerant oxygen electroreduction catalyst for mixed-reactant Swiss-roll direct borohydride fuel cells[END_REF]. With proper management of the fuel/oxidant flows and cell/electrode/separator geometry, non-tolerant catalysts can however be used without detrimental performance losses [START_REF] Aziznia | Experimental advances and preliminary mathematical modeling of the Swiss-roll mixed-reactant direct borohydride fuel cell[END_REF]. [START_REF] Olu | Evaluation of anode (electro)catalytic materials for the direct borohydride fuel cell: Methods and benchmarks[END_REF] The cathode reaction in a DBFC

As specified in the Introduction, DBFC can operate with either ORR or HPRR at the cathode. This Section briefly discusses how the choice of the cathode reaction affects DBFC performance and the criteria imposed on the cathode electrocatalysts.

Oxygen reduction reaction

The ORR (Eq.2) is the usual cathode reaction in a DBFC, O2 being advantageouslyharvested from air at no cost. Because of the alkaline anolyte and the imperfect separation brought by the membrane/separator, alkaline ORR is at stake in a DBFC; Pt and Ag-based catalysts are very active for this reaction, but are not BH4 -tolerant/selective [START_REF] Chatenet | Kinetics of sodium borohydride direct oxidation and oxygen reduction in sodium hydroxide electrolyte -Part II. O-2 reduction[END_REF]. So, they shall not be used with an AEM, that leads to consequent fuel crossover (see section 3.2). Many Aubased or Ag-based alloys were mentioned for ORR in DBFCs, but the materials are also active for the BOR, a real non-sense (see e.g. [START_REF] Wang | One-Pot Synthesis of Dealloyed AuNi Nanodendrite as a Bifunctional Electrocatalyst for Oxygen Reduction and Borohydride Oxidation Reaction[END_REF][START_REF] Wang | Bifunctional Electrocatalysts for Oxygen Reduction and Borohydride Oxidation Reactions Using Ag3Sn Nanointermetallic for the Ensemble Effect[END_REF][START_REF] Wang | Gold-Copper Aerogels with Intriguing Surface Electronic Modulation as Highly Active and Stable Electrocatalysts for Oxygen Reduction and Borohydride Oxidation[END_REF]). With a CEM, such noble catalyst can be used, even if for alkaline fuel cells like the DBFC, one rather envisions to use non-noble catalysts also at the cathode.

Non-noble catalysts are usually less active than Pt and Ag for "pure ORR" but more tolerant/selective in presence of a fuel. The literature is extremely rich in studies of non-Pt ORR catalysts, and several have been successfully demonstrated in AEM-based or separator-based DBFCs. Without being exhaustive, one can cite Fe-N-C or Co-N-C [START_REF] Sgarbi | Oxygen Reduction Reaction on Metal and Nitrogen-Doped Carbon Electrocatalysts in the Presence of Sodium Borohydride[END_REF], MnO2 [START_REF] Chatenet | Kinetics of sodium borohydride direct oxidation and oxygen reduction in sodium hydroxide electrolyte -Part II. O-2 reduction[END_REF][START_REF] Garcia | Carbon-supported nickel-doped manganese oxides as electrocatalysts for the oxygen reduction reaction in the presence of sodium borohydride[END_REF],

LaNiO3 [START_REF] Yang | A direct borohydride fuel cell with a polymer fiber membrane and non-noble metal catalysts[END_REF][START_REF] Ma | Effect of cobalt precursors on Co3O4 anodic catalyst for a membrane-free direct borohydride fuel cell[END_REF].

Hydrogen peroxide reduction reaction (HPRR)

The HPRR usually occurs in acidic conditions in H2O2-DBFCs, H2O2 being less stable in base.

Using the HPRR is advantageous in some applications where gaseous reactant are dangerous, e.g. submarines [START_REF] Wang | Efficient pH-gradientenabled microscale bipolar interfaces in direct borohydride fuel cells[END_REF][START_REF] Hjelm | Impact of the anode catalyst layer design on the performance of H2O2-direct borohydride fuel cells[END_REF]. Acid-stable Au or Au-based catalysts [START_REF] Wang | Efficient pH-gradientenabled microscale bipolar interfaces in direct borohydride fuel cells[END_REF] and Pt/C [START_REF] Hjelm | Impact of the anode catalyst layer design on the performance of H2O2-direct borohydride fuel cells[END_REF] are the norm, and more complex chemistries of catalysts were also evaluated, like Pt-rare Earths (quite active) [START_REF] Cardoso | Platinum-rare earth cathodes for direct borohydride-peroxide fuel cells[END_REF] and perovskites (poorly-performing) [START_REF] Santos | Perovskite cathodes for NaBH4/H2O2 direct fuel cells[END_REF]. Proper engineering the cathode catalyst layer and balance-of-plant of the H2O2-DBFC is critical to achieve good H2O2-DBFC performance [START_REF] Stroman | A calibrated hydrogenperoxide direct-borohydride fuel cell model[END_REF].

5 Performance, stability and durability in DBFC operation

Effect of the electrodes/diffusion medium structure

The previous sections made clear that the core materials of (H2O2-) DBFCs drive their performance; their assembly, interface and structure also have a dramatic impact, in particular for the anode: (i) cracked (porous) layers (Figure 4A, B) (ii) graded layers based on Pd/C and Pt/C catalysts (Figure 4C) [START_REF] Hjelm | Impact of the anode catalyst layer design on the performance of H2O2-direct borohydride fuel cells[END_REF] all enabled to optimize the (very complex) mass-transport processes in DBFC anodes. from [START_REF] Wang | Reactant-Transport Engineering Approach to High-Power Direct Borohydride Fuel Cells[END_REF] with permission from CellPress. (E) Adapting the Pt nanoparticles density (catalyst loading) at the surface of carbon-fiber anodes enables to control the rate of H2 escape during the BOR in DBFC; reproduced from [START_REF] Asonkeng | Synthesis of metallic nanoparticles for heterogeneous catalysis: Application to the Direct Borohydride Fuel Cell[END_REF] with permission from Elsevier.

Indeed, the BOR completion and kinetics strongly depends on the mass-transport of BH4 -/OH -/H2 to/from the catalytic sites within the porous texture of the electrode [START_REF] Braesch | Nickel 3D Structures Enhanced by Electrodeposition of Nickel Nanoparticles as High Performance Anodes for Direct Borohydride Fuel Cells[END_REF][START_REF] Abahussain | Mass-Transfer Measurements at Porous 3D Pt-Ir/Ti Electrodes in a Direct Borohydride Fuel Cell[END_REF][START_REF] Cheng | Influence of operation conditions on direct borohydride fuel cell performance[END_REF].

So, the diffusion layer upstream the anode has a marked influence on the anode performance, thin/open layers being beneficial to H2-bubbles evacuation and liquid anolyte access [START_REF] Park | Influence of anode diffusion layer properties on performance of direct borohydride fuel cell[END_REF]. The concept can be extended to the channels feeding the anolyte solution in a H2O2-DBFC:

engineering the reactant-transport within the anode flow field architecture and fuel flowrates mitigates parasitic borohydride hydrolysis and hydrogen oxidation reactions, and minimizes anode masking by hydrogen bubbles [START_REF] Wang | Reactant-Transport Engineering Approach to High-Power Direct Borohydride Fuel Cells[END_REF] (Figure 4D).

Stability of DBFC performance and durability of DBFC catalysts

Although DBFCs are still at their infancy compared to PEMFCs, some studies have evaluated their stability in operation. For example, the start/stop operation of a (CEM-based) DBFC was studied [START_REF] Ould-Amara | Operating heterogeneities within a direct borohydride fuel cell[END_REF]: using a ORR-inactive anode catalyst can prevent cell reversal issues that are often encountered in PEMFC.

From a materials view-point, operation in the high-pH environment of the anode is very detrimental to carbon-supported electrocatalysts [START_REF] Olu | Investigation of platinum and palladium as potential anodic catalysts for direct borohydride and ammonia borane fuel cells[END_REF][START_REF] Lafforgue | Selected review of the degradation of Pt and Pd-based carbonsupported electrocatalysts for alkaline fuel cells: towards mechanisms of degradation[END_REF][START_REF] Lafforgue | Degradation of Carbonsupported Platinum Group Metal Electrocatalysts in Alkaline Media Studied by in situ Fourier-Transform Infrared Spectroscopy and Identical-Location Transmission Electron Microscopy[END_REF]. Anode catalyst erosion from their substrate is often mentioned as one cause of DBFC instability [START_REF] Li | Performance degradation of a direct borohydride fuel cell[END_REF]; cathode catalyst dissolution and re-deposition at the anode, and detachment of carbon-supported nanoparticles after DBFC operation are additional explanation for the instability of PGM-based DBFCs upon prolonged operation [START_REF] Olu | Investigation of platinum and palladium as potential anodic catalysts for direct borohydride and ammonia borane fuel cells[END_REF]. Non-PGM Co-Ni-B [START_REF] Duan | Cobalt nickel boride nanocomposite as high-performance anode catalyst for direct borohydride fuel cell[END_REF] and NiB [START_REF] Li | A new application of nickel-boron amorphous alloy nanoparticles: anode-catalyzed direct borohydride fuel cell[END_REF] BOR anode catalyst were found rather active/stable in prolonged DBFC operation.

CEM stability in DBFCs is never reported as a major issue; however, the temperature strongly influences their performance in DBFC, because of a complex interplay between imperfect anode/cathode separation (and related mixed potentials), high sensitivity of Na + -ionic conductivity to temperature, BH4 --hydrolysis, and usual electrokinetic/mass-transport effects [START_REF] Olu | Evaluation of anode (electro)catalytic materials for the direct borohydride fuel cell: Methods and benchmarks[END_REF][START_REF] Ould-Amara | Operating heterogeneities within a direct borohydride fuel cell[END_REF][START_REF] Olu | Investigation of platinum and palladium as potential anodic catalysts for direct borohydride and ammonia borane fuel cells[END_REF].

There is no data reporting AEM-based stability in DBFC operation; if their hydration is properly-controlled (which is easier for DBFCs fed with a liquid-based anolyte), AEM can be fairly stable on the long-term, though, especially with CO2-scrubbed incoming air [START_REF] Serov | Hot topics in alkaline exchange membrane fuel cells[END_REF][START_REF] Mustain | Durability challenges of anion exchange membrane fuel cells[END_REF].

BPM did show 50 h-long performance-stability upon H2O2-DBFC operation [START_REF] Wang | Efficient pH-gradientenabled microscale bipolar interfaces in direct borohydride fuel cells[END_REF], and porous BPM ca. 300 h-long operation at 200 mA cm -2 [START_REF] Chen | Porous polybenzimidazole membranes with excellent chemical stability and ion conductivity for direct borohydride fuel cells[END_REF].

One clear difference between DBFCs and their H2-fed counterparts is the formation of H2 from the HER (when the anode operates below 0 V vs RHEas desired) or from catalytic decomposition of BH4 -; this H2 must be valorized as much as possible if formed (which Pt does above 0 V vs RHE), but ideally not produced. Metallic Ni is an interesting catalyst in that extent, because it enables to lower the low-potential H2 production, hence enabling higher voltage DBFC operation than Pt (Figure 4B), but is incapable to valorize the H2 it produces, leading to non-negligible H2-escape (Figure 4E). To manage properly H2 production and escape, materials strategy are advantageously complemented by engineering ones [34,[START_REF] Braesch | Nickel 3D Structures Enhanced by Electrodeposition of Nickel Nanoparticles as High Performance Anodes for Direct Borohydride Fuel Cells[END_REF][START_REF] Wang | Reactant-Transport Engineering Approach to High-Power Direct Borohydride Fuel Cells[END_REF][START_REF] Braesch | A high performance direct borohydride fuel cell using bipolar interfaces and noble metal-free Ni-based anodes[END_REF].

Concluding remarks

DBFCs are very versatile systems, which offer many possibilities in terms of usable core materials (at the anode, cathode, for the separator/membrane), fuel (liquid anolyte, whose pH and BH4 -concentration can be varied) and oxidant (gaseous O2, acidic H2O2 catholyte). Their performances are tightly linked not only to their core materials, but also to their assembly and structure: the core materials must be selected according to the operating conditions and electrode/cell structures chosen. This stimulates intense research efforts, that recently led to spectacular fundamental understanding and technical performances.

This selected review highlighted that, although many anode catalysts have been studied since the pioneering work of Amendola 20 years ago, by now, significant progress in the understanding of the complex BOR mechanism has only been achieved for rather simple catalysts (monometallic Pt-, Pd-, Au-and Ni-based). Among them, only Pt and Ni present sufficient extent of low-potential activity, though for different reasons. While Pt dissociatively adsorbs BH4 -into BHad and Had and then near-completely oxidizes Had (only above 0 V vs RHE but at a very fast rate, hence leading to faradaic efficiency close to 100% on properly-designed electrodes), Ni in its metal state is capable to catalyze anodic BH4 -oxidation without promoting the unwanted cathodic HER, hence leading to non-negligible BOR currents at potential below 0 V vs RHE. However, the BOR mechanism on Ni involves generation of significant amount of H2 that the electrode is incapable to properly oxidize; this results in non-negligible H2-escape.

In addition, the mechanisms of the BOR and its competing reactions are strongly influenced by the operating conditions of the anode. The nature of the membrane/separator has a marked influence on the DBFC performance. The choice of the membrane/separator not only defines the ionic conductivity but also affects crossover of the anolyte species (Na + for a cationexchange membrane and anionic fuel species for an anion-exchange membrane). Because of this, AEMs must be employed in conjunction with a fuel-tolerant cathode catalyst (usually nonnoble). In addition, the structure and the texture of the anode is pivotal to its proper performance, so to enable optimized mass-transport for the fuel and its numerous (desired or not) reaction products. Finally, like any other fuel cells, DBFCs are subjected to degradation issues, and these are very specific to their fuel (liquid alkaline anolyte); while PGM-based catalysts are very sensitive to these degradations, non-PGM ones (e.g. Ni-based) seem more stable, another asset of these materials for DBFC operation. The highest performances reached for a DFBC (of small geometric area)

2

  Figures 1A and B compare the BOR activities of carbon-supported metal nanoparticles (Ni/C, Pt/C, Pd/C and Au/C) in 5 mmol L -1 NaBH4 and 1 mol L -1 NaOH in a narrow and a wide potential interval, respectively. The Au/C electrode demonstrates negligible BOR current below ca. 0.3 V vs RHE, requiring application of high potentials (above 0.8 V vs RHE) to achieve mass-transport limiting current. On Pd/C, the BOR starts at ca. 0.3 V lower potential than for Au/C, but the BOR current is still negligible below 0 V vs RHE. For Pt/C, the BOR current increases abruptly around 0 V vs RHE, but the HER becomes predominant and limits the BOR efficiency below ca. -0.05 V vs RHE. In contrast, metallic Ni/C exhibits anodic BOR currents already above -0.2 V vs RHE, although the mass-transport limiting current on Ni/C is lower than on Pt/C (Figure1A). Albeit not relevant to DBFC applications, the BOR has also been investigated at high anodic potentials (Figure1B): formation of surface oxides upon anodic polarization results in attenuated BOR activity of Pt, Pd, Au, Ni, due to decreased number of surface sites available for BH4 -adsorption. The strongest effect was observed for Ni (and Ni/C):

Figure 1 .

 1 Figure 1. Ohmic drop-corrected (in dynamic mode) CV curves (A), (B) obtained for metallic NiED/C or oxidized NiOx/C (solid curve), Pt/C (dashed curve), Pd/C (dash-dotted curve), and Au/C (dotted curve), as well as for (C) NiED/C electrodes at various state of their surface in N2saturated 1.0 mol L -1 NaOH + 5 mmol L -1 NaBH4 at v = 20 mV s -1 and ω = 1600 rpm;

Figure 2 .

 2 Figure 2. (A) OCP measured on polycrystalline Au, Pt, Pd and Ni electrodes for different concentrations of NaBH4 in 1 mol L -1 NaOH at T = 20 °C and ω = 1600 rpm. (B) Ohmic dropcorrected (in dynamic mode) CVs of BOR (v = 20 mV s -1 , ω = 2500 rpm, T = 20°C) on polycrystalline Au, Pt and Pd electrodes at different concentration of NaBH4; replotted from [24] with permission from Elsiever. (C) Potentiostatic measurement of the BOR on metallic NiED/C (solid curve), Pt/C (dashed curve), Pd/C (dash-dotted curve) in N2-saturated 1.0 mol L -

Figure 3 :

 3 Figure 3: (A) Injection of liquid water at the cathode enables transient recovery of the performance during operation of a CEM-based DBFC at Ucell = 0.5 V, T = 60°C with a Pt/C cathode, because it washes the accumulated NaOH; reproduced from [31] with permission from Elsevier. (B) When the DBFC is operated with an anion-exchange membrane, the fuel (NaBH4)

Figure 4 :

 4 Figure 4: (A) Illustration of the impact of the performance of a DBFC depending on the morphology of the Pt/C-based anode active layer, all other parameters being kept identical; open macropores enable better management of the mass-transport of the liquid fuel and generated H2 bubbles; reproduced from [51] with permission from Elsevier. (B) Similar effect were observed for Ni-based anodes; reproduced from [52] with permission from Wiley-VCH Verlag GmbH. (C) Graded electrodes made of Pt/C and Pd/C were prepared for optimized H2O2-fed DBFC operation; reproduced from [48] with permission from The Electrochemical Society. (D) Illustration of reactant-transport engineering to mitigate parasitic reactions (HER, BH4 -hydrolysis) to the BOR and improve the performance of liquid-fed DBFCs; reproduced

[

  34] Z. Wang, M. Mandal, S. Sankarasubramanian, G. Huang, P.A. Kohl, V.K. Ramani, Influence of Water Transport Across Microscale Bipolar Interfaces on the Performance of Direct Borohydride Fuel Cells, ACS Applied Energy Materials, 3 (2020) 4449. ** The article shows how the mass-transfer influences the apparent performance of H2O2-DBFCs [35] N.A. Choudhury, J. Ma, Y. Sahai, High performance and eco-friendly chitosan hydrogel membrane electrolytes for direct borohydride fuel cells, J. Power Sources, 210 (2012) 358. *

  decreases the BOR currents, but also significantly increases the open-circuit potential (OCP, the potential reached at zero current) compared to metallic Ni (Figure1C). The latter can be attributed to decreased binding-energy of Had on metallic Ni adjacent to the NiOx, sites and ensuing increased rate of the HER competing with the BOR below 0 V vs RHE[9].

	This example underscores how precisely-controlled surface state is needed to reach high BOR
	activity, notably for reactive metals like Ni.
	By comprehensively-analyzing published data (comparing potentials required to reach
	a relevant current density, RDE configuration), Olu et al. benchmarked BOR activity of various
	materials [4]. Figure 1D updates such plot, constructed from low-NaBH4-concentration data (5
	or 10 mmol L -1 in most studies) for carbon-supported nanoparticles: Ni clearly outperforms all
	other catalysts (including Pt) at low potentials. Other conditions being equal, higher
	overpotentials are required to achieve reasonable BOR current on 'smooth' polycrystalline
	electrodes due to their much lower ECSA (Figures 1D versus 2B).

1.3

V vs RHE, where NiOOH species form 1

[START_REF] Oshchepkov | Recent Advances in the Understanding of Nickel-Based Catalysts for the Oxidation of Hydrogen-Containing Fuels in Alkaline Media[END_REF]

. Partially oxidizing the Ni surface not only

Table 1 .

 1 The weak BH4 -adsorption on Au leads to incomplete BH4 -dissociation into BH3,ad, accompanied with larger H2 escape in a wider potential interval but smaller surface-poisoning by strongly-adsorbed intermediates.According to DFT calculations, BH4,ad binding is intermediate on Ni(111) versus Au and Pt. The reaction path follows initial B-H dissociation followed by BH3-OH bond formation, successive B-H dissociation into BOHad, and then final B(OH)3 product formation[START_REF] Oshchepkov | Insights into the borohydride electrooxidation reaction on metallic nickel from operando FTIRS, on-line DEMS and DFT[END_REF]. On Ni surfaces covered by Had and BHx,ad species, the B-H dissociation will be hindered, affecting the reaction mechanism. BH4 -adsorption on Ni is strong-enough to allow fast adsorption but nottoo-strong to favor severe surface poisoning (typical for Pt). Had is more strongly adsorbed on metallic Ni than on Pt, resulting in slower Had oxidation and slow rate of competing HER, which is the key to achieve low BOR onset potential. The downside of Ni is its inability to valorize 8 e -'stored' in the BH4 -fuel: BOR on Ni rather occurs in a 4 e -process, producing 2 H2 per BH4 - , the exact BOR mechanism on Ni being not fully understood, yet.According to DFT calculations, Pd(111) should also catalyze the BH4 -dissociativeadsorption. However, the experimental current-potential curves are strongly affected by Pd hydrides formation, making mechanistic elucidation more difficult. DFT-calculated adsorption energies for selected adsorbates on Ni(111), Pt(111),

	Au(111) and Pd(111) at zero coverage limit
	Species	Ni (111)	Binding energy (eV) Pt (111) Pd (111)	Au (111)
	BH4*	-3.68 [9] -3.50 [25]	-	-	-1.73 [26] -1.96 [25]
	BH+3H*	-	-4.73 [27] -4.56 [25]	-3.63 [25]	-
	BH3*	-2.19	-1.94 [27]	-	-0.55 [26]
	H*	-2.81 [28] -2.94 [29]	-2.70 [28] -2.72 [29]	-2.83 [28] -2.88 [29]	-2.04 [28] -2.18 [29]
	OH*	-2.98 [28]	-2.11 [28]	-2.22 [28]	-1.56 [28]

The current increase observed above ca. 1.5 V vs RHE comprises both the high-potential BOR and the oxygen evolution reaction (OER) contributions.

The poisoning effect resulting in the current decay in Fig 2C may be accelerated by the presence of impurities in the electrolyte, especially at high NaBH4 concentration.

NaOH + 5 or 50 mmol L -1 NaBH4 at E = 0.2 V vs RHE and ω = 1600 rpm; reproduced from

Acknowledgments

This work was supported by the National Research Agency, in the frame of the MobiDiC project (ANR-1-CE05-0017). Some of the work presented herein has been performed within the framework of the Centre of Excellence of Multifunctional Architectured Materials "CEMAM" No. ANR-10-LABX-44-01. A.O. acknowledges the support from the Ministry of Science and Higher Education of the Russian Federation within the governmental order for Boreskov lnstitute of Catalysis (project AAAA-A21-121011390006-0)

Author contributions

All authors have contributed equally.


Erwan Bourrand

Luis Galárraga
email: luis.galarraga@irisa.fr

Esther Galbrun

Elisa Fromont
email: elisa.fromont@irisa.fr

Alexandre Termier
email: alexandre.termier@irisa.fr

Discovering Useful Compact Sets of Sequential Rules in a Long Sequence

We are interested in understanding the underlying generation process for long sequences of symbolic events. To do so, we propose COSSU, an algorithm to mine small and meaningful sets of sequential rules. The rules are selected using an MDL-inspired criterion that favors compactness and relies on a novel rule-based encoding scheme for sequences. Our evaluation shows that COSSU can successfully retrieve relevant sets of closed sequential rules from a long sequence. Such rules constitute an interpretable model that exhibits competitive accuracy for the tasks of next-element prediction and classification.

I. INTRODUCTION

Long sequences of symbols are ubiquitous. Examples include DNA sequences, server logs, traces of network packets, and even long texts. Discovering regularities in such sequences allows for a better understanding of the sequence generation process, and can be useful e.g., for diagnostic and prediction.

Some models, such as LSTMs [START_REF] Hochreiter | Long Short-Term Memory[END_REF], excel at detecting those regularities and use them for accurate prediction. On the downside, such models are hardly understandable by human users. Models based on pattern mining, in contrast, provide highlevel human-readable descriptions of the underlying structure of the data. However, this interpretability typically comes at the cost of a restricted predictive power. We focus on the latter category of models, since we are interested in prediction but also in knowledge discovery.

In the realm of pattern mining, sequential rules are a wellestablished model for understanding and predicting sequential data. Sequential rules take the form A ⇒ C, where both the antecedent A and the consequent C are sequences of items, e.g., events, nucleotides, or words. A confidence score is often attached to the rule to measure how likely it is to observe C after A in the sequence. For instance, the rule A 1 A 2 A 3 ⇒ PowerFail with confidence 80% tell us that there is a four in five chance of undergoing a power failure after having observed the sequence of alarms A 1 , A 2 and A 3 . This can be used both for prediction, i.e., to issue an early warning, and for diagnostic, i.e., to identify the link between the alarms and the power failure.

While sequential rule mining has been extensively studied in the literature [START_REF] Fournier-Viger | A Survey of Sequential Pattern Mining[END_REF][START_REF] Cule | Mining Association Rules in Long Sequences[END_REF][START_REF] Fournier-Viger | Using Partially-Ordered Sequential Rules to Generate More Accurate Sequence Prediction[END_REF][START_REF] Fumarola | CloFAST: Closed Sequential Pattern Mining Using Sparse and Vertical Id-lists[END_REF][START_REF] Fournier-Viger | ERMiner: Sequential Rule Mining Using Equivalence Classes[END_REF], two major issues remain. First, the vast majority of approaches consider a database of short sequences rather than a long sequence. While a long sequence can always be split into a database, this incurs a loss of information at the boundaries. Second, to the best of our knowledge, no approach for sequential rule mining addresses the so-called pattern explosion, the fact that millions of sequential rules may be produced due to the combinatorial search space.

We propose the first sequential rule mining approach that takes as input a long sequence and outputs a compact set of rules. The selection of the rules is based on the principle of Minimum Description Length (MDL), a paradigm that has proved effective for model selection in pattern mining [START_REF] Vreeken | Krimp: Mining Itemsets that Compress[END_REF][START_REF] Tatti | The Long and the Short of It: Summarising Event Sequences with Serial Episodes[END_REF]. MDL approaches rely on an encoding scheme. Ours is presented in Section IV, along with our algorithm to mine rules, in Section V. Experiments, presented in Section VI, demonstrate the relevance of the rules found, as well as their predictive power for the tasks of next-element prediction, and classification for long sequences.

II. BACKGROUND

Our work stands at the crossroads of sequential and MDLbased pattern mining. Below we give brief overviews of these two fields, in turn. Sequential Pattern Mining. Mining sequential patterns on data is a well-studied problem that has given rise to a plethora of methods accounting for different notions of patterns. The vast majority of approaches assume a database of sequences as input, where sequences are ordered collections of itemsets. We refer the reader to the survey in [START_REF] Fournier-Viger | A Survey of Sequential Pattern Mining[END_REF] for a detailed account.

Among the most recent works, Fumarola et al. [START_REF] Fumarola | CloFAST: Closed Sequential Pattern Mining Using Sparse and Vertical Id-lists[END_REF] mine frequent closed sequences, i.e. sequences of maximal length such that any extension will inevitably have lower support. Closed sequences can alleviate pattern explosion to some extent as they are a subset of frequent sequences. Other approaches [START_REF] Fournier-Viger | Using Partially-Ordered Sequential Rules to Generate More Accurate Sequence Prediction[END_REF][START_REF] Fournier-Viger | ERMiner: Sequential Rule Mining Using Equivalence Classes[END_REF][START_REF] Fournier-Viger | RuleGrowth: Mining Sequential Rules Common to Several Sequences by Pattern-growth[END_REF] mine sequential rules of the form A ⇒ C where A and C may be itemsets [START_REF] Fournier-Viger | ERMiner: Sequential Rule Mining Using Equivalence Classes[END_REF][START_REF] Fournier-Viger | RuleGrowth: Mining Sequential Rules Common to Several Sequences by Pattern-growth[END_REF] or sub-sequences [START_REF] Fournier-Viger | Using Partially-Ordered Sequential Rules to Generate More Accurate Sequence Prediction[END_REF] with the constraint that C occurs after A. Itemsets are generally easier to mine than sequences, however they are less expressive because they do not account for items' order of appearance. Still, none of these methods is directly portable to long sequences as they all assume the data has been partitioned into small sequences (and hence often rely on a different definition of support). A few methods [START_REF] Cule | Mining Association Rules in Long Sequences[END_REF][START_REF] Gupta | Mining Quantitative Association Rules in Protein Sequences[END_REF] can natively mine rules on long sequences. Unfortunately, such methods are not resilient to pattern explosion and are limited to association rules between itemsets, thus they do not capture the order between items within the antecedent and the consequent. Mining patterns with an MDL criterion. The principle of Minimum Description Length (MDL) [START_REF] Grünwald | The Minimum Description Length Principle[END_REF] is a criterion rooted in information theory that stipulates that the best model for a dataset is the model that compresses it best. For a dataset D and a family of models H, the best model for D, according to the (two-parts) MDL, is the one that minimizes the description length

H * = arg min H∈H L(H) + L(D|H) , (1)
where L denotes code length in bits. Equation [START_REF] Hochreiter | Long Short-Term Memory[END_REF] strikes a balance between model complexity, as measured by L(H), and fitness to the data, as measured by L(D|H). When applying MDL to pattern mining, a model is a collection of patterns, e.g., itemsets [START_REF] Vreeken | Krimp: Mining Itemsets that Compress[END_REF], sequences [START_REF] Tatti | The Long and the Short of It: Summarising Event Sequences with Serial Episodes[END_REF] or, in our case, sequential rules. One of the main ingredients of any MDL-inspired approach is the encoding scheme, namely, the protocol to encode the data with the patterns and to encode the patterns themselves. Once an encoding mechanism is in place, we can generate candidate sets of patterns, calculate the corresponding code lengths, and select the set H * resulting in the shortest description length. KRIMP [START_REF] Vreeken | Krimp: Mining Itemsets that Compress[END_REF] was one of the pioneering efforts to apply MDL to pattern mining, more specifically to itemset mining. Given a (large) collection of itemsets mined from the data, KRIMP selects a small representative subset. The selected itemsets were also empirically shown to be effective for classification. Recently, Fischer and Vreeken [START_REF] Fischer | Sets of Robust Rules, and How to Find Them[END_REF] proposed an approach to mine compact sets of rules from data without the sequential dimension. The approaches proposed in [START_REF] Bertens | Keeping it Short and Simple: Summarising Complex Event Sequences with Multivariate Patterns[END_REF][START_REF] Bhattacharyya | Efficiently Summarising Event Sequences with Rich Interleaving Patterns[END_REF] extract sequences with gaps (but not rules) from univariate and multivariate long sequences. Unlike KRIMP [START_REF] Vreeken | Krimp: Mining Itemsets that Compress[END_REF], they combine the generation and selection of candidate patterns, which boosts efficiency and pattern quality. Shokoohi-Yekta et al. [START_REF] Shokoohi-Yekta | Discovery of Meaningful Rules in Time Series[END_REF] draw inspiration from the MDL principle to mine sequential rules from time series discretized into an integer domain. A mining approach tailored for the streaming setting is proposed in [START_REF] Yan | SWIFT: Mining Representative Patterns from Large Event Streams[END_REF], but its compliance with the MDL principle is debatable.

III. DEFINITIONS AND NOTATION

A sequence S of length n over an alphabet Σ is an ordered collection of n occurrences of symbols from Σ. We denote by S[i] the i-th element in S (1 ≤ i ≤ n), and let S[i, j] denote the contiguous sequence S[i] . . . S[j] when 1 ≤ i ≤ j ≤ n or the empty sequence ∅ otherwise. For simplicity, we write the sequence σ 1 , σ 2 . . . σ k as σ 1 σ 2 . . . σ k . We denote the concatenation of two sequences by ⊕.

We say that sequence S is a subsequence of S (respectively S is a supersequence of S ), denoted as S S, iff there exist i and j in [1, n] such that S = S[i, j]. Then, we call S[i, j] a match of S in S. More specifically, we denote by S i S the fact that S is a subsequence of S with a match starting at position i, i.e. S = S[i, i + |S | -1], and by S j S the fact that S is a subsequence of S with a match ending at position

j, i.e. S = S[j -|S | + 1, j].
The support of a subsequence S in S, denoted by supp S (S ), is the number of distinct matches of S in S, that is, supp

S (S ) = |{i ∈ [1, n] : S i S}| = {j ∈ [1, n] : S j S} . Finally, a sequence S is closed in S if there is no supersequence S
S in S such that supp S (S ) = supp S (S ).

Example 1: Sequences. Given the sequences S = abceabcadeab and S = abc, S 1 S, S 5 S, S 3 S and S 7 S are all true, hence supp S (S ) = 2.

A rule is a pair of sequences (A, C) over alphabet Σ, such that C = ∅. It is denoted as A ⇒ C. A and C are called the antecedent and the consequent of the rule, respectively. A rule such that A = ∅ and |C| = 1 is called a singleton rule. The set of singleton rules over alphabet Σ is

Ψ Σ = {∅ ⇒ σ : σ ∈ Σ}.
A rule R : A ⇒ C triggers on sequence S at position i, denoted as R i S, iff the antecedent has a match in S ending at position i, i.e., iff A i S. The rule R applies on sequence S at position i, denoted by R i S, iff the antecedent has a match in S ending at position i and the consequent has a match in S starting at position i + 1, i.e. if A i S and C i+1 S.

Clearly, R i S implies R i S.
The support of a rule is the number of times it applies in the sequence, whereas its confidence is the ratio of the number of times the rule applies to the number of times the rule triggers:

supp S (R) = |{i ∈ [1, n] : R i S}| and conf S (R) = |{i ∈ [1, n] : R i S}| |{i ∈ [1, n] : R i S}| .
Example 2: Rules. In sequence S from Example 1, rule R : ab ⇒ c has support supp S (R) = 2 and confidence conf S (R) = 2/3, because R triggers at positions 1, 5 and 11 but only applies at positions 1 and 5.

Given a sequence S up to position m and a rule R : A ⇒ C, we say that R is active at stage j (0 ≤ j < |C|) and predicts C

[j + 1], if A ⊕ C[1, j] = S[m -|A| -j, m]
. This corresponds to cases where the antecedent of R is followed by the first j elements of its consequent (empty in case j = 0) in S. Formally, we define the predicates active(R, S, j), to indicate that rule R is active on sequence S at stage j, and predict(R, S, j), to return C[j + 1] if active(R, S, j) is true.

IV. ENCODING SCHEME

To illustrate our encoding scheme, we resort to a senderreceiver metaphor, where the sender first transmits a set of rules and their corresponding weights, followed by a sequence of code words, one for each element of the sequence, in such a way that the receiver can reconstruct the original sequence.

Encoding a Sequence via Sequential Rules. Assume we want to predict the next element after cabba, based on two rules R 1 : abba ⇒ b and R 2 : ba ⇒ cd. If the confidence of R 1 is higher than the confidence of R 2 , we would guess that b is more likely than c to appear next. We rely on this simple principle to encode a sequence element by element using a set of sequential rules. Assuming the receiver knows the set of rules and their confidence, as represented by weights, as well as the history of the sequence decoded so far, they can compute a probability distribution over the possible next elements. Hence, the sender can represent the next element as a code word chosen according to this probability distribution. If the set of rules effectively produces a probability distribution concentrated on the element that indeed occurs next, the code word for that element will be short, allowing for a concise representation of the input sequence.

Given a sequence S of m elements seen so far, and a set of weighted rules (A R ⇒ C R , w R ), such that A R , C R , and w R are respectively the antecedent, the consequent, and the weight of rule R, our goal is to compute the probability of the next element given this set of rules -denoted by R. This amounts to computing a probability distribution over Σ. For each possible next element σ ∈ Σ, we sum the weights of the active rules that predict σ and divide by the sum of weights of all active rules: Hence, the overall code length for the full sequence is

P R,S (σ) = (R,j)∈A S,σ w R (R,j)∈A S w R where A S = {(R, j), (R, w R ) ∈ R s.t. active(R
L(S|R) = m∈[1,n] -log 2 P R,S[1,m-1] (S[m]) . (2)
The receiver, having the same collection of rules R and previous elements of the sequence, can perfom the same computation to dynamically reconstruct the code at his end, and decode the transmitted element, using an agreed canonical order on the alphabet to break ties if necessary.

To ensure comparability, the models must achieve lossless compression. For this reason, by construction our models always contain the singleton rule set Ψ Σ . This way, every symbol of the alphabet receives a non-zero probability of occurrence at any step, and can hence be transmitted. In fact, the singleton rule set constitutes the basis of the simplest possible model, what we call the empty model and denote by R ∅ , since it does not contain any proper rule. To each rule R σ ∈ Ψ Σ we associate a weight equal to the background probability of the predicted element, estimated as its frequency in the sequence,

f σ = |{i ∈ [1, n] : S[i] = σ}| /n.
Encoding the Rules. For the receiver to have access to the rules R, the sender must transmit the antecedents, consequents, and weights at the start of the exchange. The antecedent and consequent are subsequences, hence they can be encoded simply by stating the length of the sequence then listing their elements using codes of length -log 2 (f σ ), in order. The weight, on the other hand, is a real number of bounded precision in (0, 1). Each weight is written as a finite list of decimals that we encode by applying universal coding to the integer value obtained by listing these decimals in reverse order. Put differently, we encode weight w = 0.d

1 d 2 d 3 ...d k with a code word of length L D (w) = L N (d k ...d 3 d 2 d 1 ). L N (z)
is the length of the code word assigned by the universal code to integer z, which is such that L N (z) = log * 2 (z) + log 2 (c 0 ), with c 0 a constant adjusted to ensure the Kraft inequality is satisfied. This penalizes weights by the number of significant digits they contain rather than by their value. Overall, the code length for a rule R is the sum of the lengths of the code words for the antecedent, the consequent and the weight, respectively:

L(R) =   L N (|AR| + 1) + σ∈A R -log 2 (fσ)   +   L N (|CR|) + σ∈C R -log 2 (fσ)   + LD(wR) .
We encode a rule table by stating the number of rules and then listing them:

L(R) = L N (|R|) + R∈R L(R) . (3)

V. THE COSSU ALGORITHM

We now introduce an algorithm to mine a set of sequential rules that compresses the input sequence well under the encoding scheme presented in Section IV. Finding such a set of rules is intractable in practice, thus we resort to heuristics.

Our COSSU (COmpact Sets of Sequential rUles) algorithm is outlined in Algorithm 1. Given a sequence S over alphabet Σ as input, COSSU returns a set of rules R in two phases. First, rule construction (lines 1-2) generates a collection of candidate rules C, which are then evaluated during rule selection (lines 3-10).

Rule Construction. COSSU starts by extracting closed frequent subsequences by applying an off-the-shelf sequence miner [START_REF] Tatti | Mining Closed Strict Episodes[END_REF] to the input sequence S with a minimum support threshold of 2. Sequential rules are then generated from the sequences by considering all possible partitionings into an antecedent and a non-empty consequent. We use the compression gain as a rough estimate of the individual ability of a rule to compress the sequence:

gain(R) = confS(R)•supp S (R)•L(CR)-(L(AR)+L(CR)) . (4)
This score puts in balance the potential benefit and cost of adding the rule to the rule set. The benefit depends on how often the consequent is correctly predicted (first term), whereas the cost is the code length of the rule's antecedent and consequent (second term). The latter term constitutes a lower bound on the cost, with a weight yet undetermined. At if L(R , S) < L(R, S) then

7: R ← R 8: for R ∈ R \ R ∅ do 9: if L(R \ {R }, S) ≤ L(R, S) then 10:
R ← R \ {R } 11: return R the end of this first phase, the set of candidates consists of those rules that have a strictly positive compression gain.

Rule Selection. COSSU resorts to a greedy strategy to build the rule set R. Initially, R consists of the singleton rules (line 3). The algorithm then processes the candidate rules in C by order of decreasing compression gain, i.e. from most promising to least promising (line 4). The candidate rule is tentatively added to the rule set and the weights are re-adjusted (line 5). If the resulting rule set yields better compression than the current one, the current set is replaced (line 7) and the algorithm goes into a pruning loop. Otherwise, the rule is discarded and the algorithm moves on to the next candidate. The pruning loop (lines 8-10) checks whether the newly added rule makes any of the previously incorporated non-singleton rules obsolete. To do so, it tentatively removes each of the rules in turn and checks whether the compression improves as a result, in which case the rule is permanently removed from R.

Adjusting Rule Weights. Given a set of selected rules, COSSU must determine a suitable vector of weights w associated to the rules, so as to optimize the code length of both the model L(R) (complexity) and the sequence L(S|R) (fit). Because optimizing both aspects concurrently is very challenging, we assume that the code length of the weights is fixed, by fixing the floating point precision of the weights, and focus on the problem of minimizing L(S|R), i.e. solving arg min

w m∈[1,n] -log 2 P R,S[1,m-1] (S[m]) .
We do so greedily, by adjusting the weight of each rule in turn, while keeping the value of the other weights fixed. The minimization resorts to the golden section search algorithm [START_REF] Kiefer | Sequential Minimax Search for a Maximum[END_REF], initializing the weights to 1. In the end, we scale all weights to ensure that their values lie in the interval (0, 1). Designing an algorithm that is able to optimize both L(R) and L(S|R) is a major direction for future work.

VI. EVALUATION

We evaluate our proposed algorithm on both synthetic and real-world datasets. For real data, we evaluate the rules learned by COSSU by using them as features in two classical machine learning tasks on long sequences: next event prediction and classification. While COSSU is not designed specifically for these tasks, it still yields acceptable performance and reports rules that capture useful patterns in the data. A full account of our experiments is available in an extended version [START_REF] Bourrand | Discovering Useful Compact Sets of Sequential Rules in a Long Sequence[END_REF] of this paper.

A. Evaluation on synthetic data

To study the behaviour of our algorithm in controlled settings, we generate synthetic random sequences of symbols and inject patterns that match a set of hand-crafted sequential rules. Then, we verify whether COSSU is able to recover the planted rules. We show in [START_REF] Bourrand | Discovering Useful Compact Sets of Sequential Rules in a Long Sequence[END_REF] that COSSU can distinguish between regularities and background noise in long sequences.

B. Evaluation on a prediction task

Next, we used the rules mined by COSSU to predict the next event in the sequence and showed that the achieved performance competes with interpretable methods for nextelement prediction such as bigrams and Hidden Markov Models (HMM).

C. Evaluation on a classification task

In this experiment, we use the following datasets: Quantified Awesome is a life log1 that records the daily activities of its owner, an enthusiast of the "Quantified Self" movement, since 2011; we predict whether a sequence of events happened on a weekday or during the weekend; Presidential debates consists of 555 sentences uttered by Donald Trump and Hillary Clinton in the context of the 2016 US election; the goal is to predict the speaker given a sentence2 ; Newsgroups is a dataset of 180 posts about the topics electronic and religion3 ; Film critics is a dataset of 1800 movie reviews used for sentiment analysis 4 ; Stylometry is a database of 2000 writings from H.P. Lovecraft or E.A. Poe, where the goal is to predict the author based on its writing style 5 ; Stylometry (PoS) is the sequence of part-of-speech tags from the previous dataset. For all datasets (except Quantified Awesome), our alphabet Σ consists of all the words present in the corpus after removing special characters and stop words, and stemming of the remaining words. All datasets were split into training, validation, and test subsets. Experimental setup. In line with the MDL-based classifier proposed in [START_REF] Vreeken | Krimp: Mining Itemsets that Compress[END_REF], we can use COSSU to classify sequences as follows: For each class c, we build a training sequence by concatenating all the sequences labeled with c. We then extract sets of rules with COSSU on the resulting long sequence. This set of rules defines a model H c that characterizes the generation process for sequences in class c. To predict the class of an input sequence S, we compute the description length L(S|H c ) for each class c and return the class that compresses S best, i.e., the class that minimizes L(S|H c ).

We compare the COSSU classifier to (i) an SVM classifier trained on a bag-of-words representation of the text instances, (ii) an HMM-based classifier, and (iii) logistic regression trained on top of the BERT language model [START_REF] Devlin | BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding[END_REF]. Results. Despite not being a native classifier, COSSU achieves the best performance on three of the experimental datasets, and exhibits comparable performance to HMM and state-of-theart text classifiers. Furthermore, and unlike its competitors, COSSU is inherently interpretable because its rules serve as an explicit explanation for the outcome of classification. VII. CONCLUSION We have presented COSSU, an algorithm to mine sequential rules from a long sequence of symbolic events. Our approach is inspired by the MDL principle and retrieves a compact and relevant set of rules. Experiments on real-world data show that, in addition to providing an interpretable model for sequential data, the retrieved rules achieve competitive accuracy on the tasks of next event prediction and classification, as compared to other symbolic methods.

As future work, we would like to design a procedure to optimize the weights of the rules while dynamically adjusting their precision. We would also like to allow our method to handle gaps, perhaps by taking inspiration from [START_REF] Tatti | The Long and the Short of It: Summarising Event Sequences with Serial Episodes[END_REF].

  , S, j)}, and A S,σ = {(R, j) ∈ A S s.t. predict(R, S, j) = σ}. A full sequence S of length n is transmitted element by element. At each step m, we encode the next symbol S[m] with a code word chosen according to the probability assigned to it based on R and the portion of the sequence seen so far, S[1, m -1].

Algorithm 1

 1 COSSU: finding a compact set of sequential rules Require: A long sequence S of elements over an alphabet Σ Ensure: A compact set of sequential rules R 1: S ← MineClosedSequences(S) 2: C ← {R ∈ PrepareRules(S), R ∈ ΨΣ and gain(R) > 0} 3: R ← R ∅ , with adjusted weights ˆ w = arg min w L(S|R ∅ ) 4: for R ∈ C, ordered by decreasing gain(R) do 5: R ← R ∪ {R}, with re-adjusted weights ˆ w = arg min w L(S|R ) 6:

  As anecdotal examples, we show a few rules characterizing the classes of the Stylometry dataset: E.A. Poe: rue → morge ourang → outang little old → gentleman H.P. Lovecraft: pnakotic → manuscript catch eight → clock coach arkham necronomicon mad → arab abdul alhazred

http://quantifiedawesome.com/records

https://www.kaggle.com/mrisdal/2016-us-presidential-debates

https://kdd.ics.uci.edu/databases/20newsgroups/20newsgroups.html

https://is.gd/rdx39u

https://bit.ly/3wBqITA

Acknowledgements. The authors would like to thank Nikolaj Tatti for providing a fast implementation of a closed gapless sequential pattern miner.


Laure Emperaire

Dominique Guillaud

Nicolas Césard

Between development policies and narratives of origin: an exploratory approach of biodiversity in Ataúro (Timor-Leste)

Introduction

A century apart, two documents discuss Ataúro island's future. In 1916, the infantry captain Antonio Leite de Magalhães published A Ilha de Ataúro, Noticia sobre a ilha e seus habitantes seguida de vocabulário, a 24-page opuscule printed in Macau. While acknowledging the limited scope of his observations, Magalhães did not hesitate to describe the fauna and flora as "extremely poor", except for the diversity of birds and fish. About thirty spontaneous or cultivated plant species of high economic value captured his attention and they were designed by their Portuguese name, and by their local denominations in Ratlungu or in Resuk. This was probably the first economic botany inventory in the island. Agricultural and artisanal practices were also briefly described. As future steps towards the island's development, he suggested to strengthen Portuguese infrastructures, to develop trade and agriculture based on coconut trees, areca, tobacco, various fruit species, and to encourage rice and corn production as food crops. As sources of wealth that would allow capitalização, he mentioned the sale of dried fish and pearls, as well as beeswax and swallow's nests, other high value products. With these measures in place, Ataúro would cease to be a null in the province's economic balance1 (Magalhães, 1916: 24).

A century later, the island's population has grown from about 5,000 to 8,000 inhabitants, and its future is discussed in the Plano de Ordenamento do Território da Ilha de Ataúro approved in 2016 by the Council of Ministers (ZEEMS-TL, 2015). This plan focuses on tourism linked to biodiversity, whether marine -with diving and snorkeling -or terrestrial, with hiking activities and village stays. The planned infrastructures, today not yet implemented, respond to a wide range of tourist practices, from seaside resorts to eco-tourism. In addition to the marine diversity, the diversity of plants on the island provides the setting for a tourist scene that combines beauty and variety of landscapes with local emblematic productions, whether traditional or recent (wood carvings, basketry, fibre weaving or products appreciated by tourists such as coconuts) [START_REF] Guillaud | Entre pétrole et tourisme, la conservation participative des patrimoines locaux au Timor-Leste[END_REF]. A new capitalização is now being based on local biodiversity as an economic resource, although it only marginally considers its local meanings and values.

While the state of East Timor, by promoting handicrafts and emblematic places, invests significantly in heritage policies as a lever for tourism, biodiversity is still struggling to emerge as a cultural asset.

In Ataúro, it remains primarily an object of conservation with protected areas such as the Manukoko Reserve (4,000 ha) or a source of raw materials for emblematic products such as tais and other weavings, with vegetable dyes and fibers, wooden sculptures, etc. However, the biodiversity of Ataúro and of other Timorese regions represents a heritage with both tangible (biological) and intangible (knowledge and other associated cultural references) components that cannot be dissociated.

Moreover, in a context of great ecological vulnerability and in front of a globalization that generates its own models of development, it is urgent to recognize the role of local populations which, through their practices and knowledge, contribute to the existence of a biodiversity embedded in the society and its territory (Diaz et al., 2019;[START_REF] Reyes-García | The contributions of Indigenous Peoples and local communities to ecological restoration[END_REF]. In that perspective, the objective of this paper is thus to show how the relationships that links society and biodiversity in Ataúro are an integral component of the island's intangible cultural heritage.

Studies on the relations between plants and societies are relatively few in Timor-Leste and, to our knowledge, absent on Ataúro, except for Hull's botanical linguistics work ( 2006) which mentions about twenty main cultivated plants, or for scattered data such as Magalhães'. The data presented here were collected between 2016 and 2018 during three fieldtrips of about ten days each in the region of Makadade2 , located in the south-central part of the island, near the sacred summit of Manukoko. They result from observations and short interviews carried out during different explorations of the surrounding areas and from more systematic surveys of cultivated species in the to'os. We gathered a corpus of data on about a hundred spontaneous or cultivated species, with their vernacular names, and they have been partly identified on the basis of photographs (but we did not collect any material). These data on the plants complement the extensive investigations carried out in Makadade and Makili about the origin narratives of the different social groups of Ataúro and about their territoriality.

From biodiversity to intangible cultural heritage

In Ataúro, four main reading keys can be primarily discerned to organize the material and immaterial components of vegetal biodiversity in their relationship to society: the theme of origins -whether the beginnings of the island or more recent history -, the treatment of spontaneous or cultivated plants, the treatment of plants as material and immaterial resources, and finally the social practices on which is based such management of plants. These are the key themes on which we have based our work, although relations between society and the vegetal realm is naturally more complex, and other interpretations are also possible.

Origins and temporality of plants

Plants are omnipresent in the narratives about the origin of the island and its cultural diversity, and they punctuate the stages of its material and social constitution. To make a quick summary, the ficus muung (Ficus cf. variegata) was the first tree of humankind on the very small island of Manukoko. A pig which ate its fruits metamorphosed into a woman and gave birth to three boys. One day they went out to fish with a fish trap was brought back filled with all kind of leaves and bamboo, thus signaling that space was no longer marine but terrestrial. These three brothers, at the origin of the linguistic diversity of the island, tested the magic of their arrows by shooting and killing the muung tree, before raising Ataúro from the sea. As they explored the island, they left a watermelon and a citrus in the localities of Bikeli and Doru, which turned into two women who married a man, resulting himself from the transformation of a sheath that the brothers also left on their way in Abak [START_REF] Guillaud | Les narrations d'Atauro (Timor Est)[END_REF].

Several clan (or houses, lisan3 ) names refer to plants: the hae (lari -Imperata cylindrica) and the fafulu (luli -Bambusoideae) are respectively at the origin of Ruma Lari in Makadade and Luli in Makili. In other localities of the island, plant names such as ai-kfau or haru (Hibiscus tiliaceus), haas or ah'ran (Mangifera sp.), ai-sukaer or ana'r (Tamarindus indicus), hali or muung (Ficus cf. variegata) designate groups of descendants. Other phytonymes such as ai-dak or i-leti (Schleicheria oleosa) refer to places. Sacred Ficus are associated with emblematic places, springs, rock shelters etc. Individuals of other plant species as i-mera (n.i.4 ), i-puti (Gyrocarpus americanus), laraho (n.i.) also fall within this area of the sacred. In the past, the market in Makadade used to take place under a ficus before being moved to the center of the village of Anartutu. Both species and plant individuals are cultural and territorial markers.

The origin of the plants that are mentioned is an important element in their identity. There is a clear partition between cultivated plants from ancient and present times. Sorghum, batar-ain-naruk (Sorghum bicolor), millet or tora (Setaria italica) and tears of job, batar-fatuk (Coix lacryma-jobi), are ancient cultures but are still cultivated in some places. These cereals have been largely replaced by maize with varieties that are now considered as local, with the recent addition of so-called improved varieties. The geographical origin of the plants is frequently mentioned: a type of sinkomás (Pachyrhizus sp.) is considered to come from Australia; a bean (Vigna umbellata) was lost and then reintroduced from Indonesia; the anteriority of bitter cassava over sweet cassava (which would have been brought to Makadade from the village of Arlo) is affirmed; shade plants were introduced by the Portuguese, others by the Indonesians, etc. Invasive plants also have a meaningful origin: Lantana camara (ilau karuk) and Chromolaena odorata (aper hatu) are said to have originated from an illadvised attempt by the United Nations to replace hae (Imperata cylindrica) in which rats swarmed, destroying the crops. This account is partly in line with the official history of these invasive species because even if their introduction was fortuitous, C. odorata does competes with I. cylindrica by rapidly overtopping itand it is itself eliminated by another introduced and invasive species, the aikafé (Leucaena leucocephala) (McWillliam, 2000). Therefore, the plants' history in Ataúro draws from different registers, that of the narratives of origin, and that of the circulation of cultivated (and invasive) plants, which followed the settlement routes and is also part of the recent or current history of the island.

Cultivated and spontaneous plants

The report of a soldier published in the Boletim de Comércio, Agricultura e Fomento da Província de Timor of 1915-1916 mentions that in Ataúro "... most of the indigenes didn't have hortas. Those on the coast lived on fish, palm juice, and some maize; they did not grow themselves maize but sailed to Dili to procure it in exchange for the fish that they caught. They told me that they didn't need hortas because the sea was their horta -it gave them fish to eat and to exchange for maize aplenty. But I made them open as many hortas as they could so that they have something to eat without having to go to other localities to acquire goods except in times of need." (BCAeF, 1915-6: 738 apud Sheperd & Palmer, 2015, p. 294). This episode takes place at the beginning of the 20th century at a time when the cultivation of maize (introduced on the island of Timor around the end of the 17th century - [START_REF] Dampier | A voyage to New Holland[END_REF]in Shepherd & Palmer, 2015), and of rice, were strongly encouraged, if not made compulsory by the central government. The quote highlights the importance of exchange networks with the main island, in ways that need to be clarified, and the invisibility, for the Portuguese, of local production systems, of their spatial organization and of cultivated species. This episode also suggests that in Ataúro the importance of maize has increased sharply over the course of the 20th century. Today, it represents the staple food in the island, along with pigeon pea, and it has supplanted sorghum and millet, two cereals that are now rarely cultivated and are considered as ancestral crops.

Today's agricultural model in the Makadade highlands is that of a slash-and-burn agriculture in small plots enclosed by stone walls. Each family has three to four of these to'os to ensure a food autonomy that is submitted to strong annual and interannual climatic variations, and is supplemented by selling and exchanging staples for fish mainly with Berau (a settlement on the coast). The diversity of cultivated plants is high, with several varieties of pigeon peas or tunis (Cajanus cajan), varieties of maize, beans of various species, sweet potato, yam-bean or sinkomás (Pachyrhizus erosus), etc.

Various ligneous species, moringa, papaya or ai-dila, annone or ai-ata, tamarind tree, and others are grown here for food, medicinal or technical purposes. Ai-lele (Ceiba pentandra) is cultivated for its young edible fruits and for its fiber; ai-kfau (Hibiscus tiliaceus), very common near the dwellings, provides fibers formerly used in the manufacture of loincloths; ai-dak (Schleicheria oleosa) is omnipresent for its edible oleaginous fruits. As an example, a plot of 400 to 500 m 2 near Makadade included 33 cultivated species, herbaceous or arboreous. Two main groups of plants are found there, the oldest ones, mainly banana, coconut, Araceae and Dioscoreaceae and some local trees as ai-dak, and those introduced since the sixteenth century [START_REF] Erskine | Wild plant food in Timor-Leste[END_REF].

These cultivated species are but one aspect of the productive system that incorporates equally important non-cultivated resources. At the forefront of these is the palm Borassus flabellifer, the tua which provides the above-mentioned palm wine, actively consumed throughout the year and a central ingredient of local sociability. The fruits are consumed in May -June, the fibers from the leaves are an essential raw material for traditional basketry, and the petioles have many uses, for example to reinforce fences. Palm juice may have constituted an important resource to compensate for the lack of water on the island [START_REF] Guillaud | Les narrations d'Atauro (Timor Est)[END_REF]Guillaud et al., 2015). The tua-metan (Arenga pinnata), a palm from the humid forests, provides palm wine, but with lower yields and higher fermentation. The aitali's (Corypha utan) fiber is used for weaving the local tais hrapin hirik and also provided a starch, which later has been substituted by cassava.

Beans are another group that combines the spontaneous with the category koto moruk (bitter beans) and the cultivated with the fore. In fact, all of them are cultivated, at least in the situations we have observed, although the koto reseed on their own in the fields. The preparation of beans is very laborious: they have to be washed several times and require a long cooking time and therefore a lot of wood fuel. Both are mixed together when consumed.

Outside cultivated area, forest resources, considered as pertaining to ancient times, are used in periods of scarcity or conflict. Kumbili (Dioscorea cf. esculenta), a spontaneous but probably formerly cultivated plant in South-East Asia [START_REF] Purseglove | Tropical crops. Monocotyledons[END_REF], yields large tubers sold on the local market.

There are several species of mango trees, including haas (Mangifera indica) and wild mango (Mangifera spp.), probably once a food resource and now a territorial marker. The vine kaleik (Entada sp.) produces large flat seeds that must be boiled several times before eating. The trees eri (n.i.), elas (Ficus sp.), and meam (n.i.) provide edible fruits, that were traded in the past with the even more precarious people of Bikeli. The status of another group of species, used for food or others, is between protection and cultivation: ai-kiar, Canarium spp., ai-kamii, Aleurites moluccana, ai-hanek, Alstonia scholaris, ai-dila, Aegle marmelos among others. The hae (Imperata cylindrica), which invades fallow land, is also a key resource because it is used as thatch. The replacement of this biological material by zinc sheets results in the uncontrolled spreading of this herb, thus modifying the agricultural cycle in which a productive plot of land and a useful fallow land followed one another.

Therefore, the confrontation of spontaneous 5 vs. cultivated plants does not reflect the functioning of the food system, nor the way in which biodiversity resources were organized according to their uses.

Such system was based on a singular arrangement of resources from the forest and from the to'os, as well as a frequent multifunctionality of resources; such a vision is opposed to that of the state which sees a compartmentalization between rights and rules, spaces and practices [START_REF] Mcwilliam | Hunting and Harvesting the commons[END_REF].

Plants and their uses

The various domains of material culture rely to a large extent on local plant resources, timber with hardwood species for house construction (ai-na, Pterocarpus indicus, ai-heu, Garuga floribunda, aibesir, Intsia bijuga...), for the manufacture of dugout canoes (ai-lele, Ceiba pentandra), ai-sukaer (Tamarindus indica) for tool handles, ai-bubur (Eucalyptus alba) for the wood that fuels the forge, etc.

One dye used for the ai-tali's (Corypha utan) fiber mats is given by ai-tururo (Sesbania grandiflora).

The wooden plates of Makadade, a traditional exchange item within the island and today a commercialized craft product, are made from the wood of the already mentioned ai-hanek (Alstonia scholaris), a species frequent in the to'os. The fruit of ai-ua (Barringtonia asiatica) is ichtyotoxic, like the roots of a Derris (or Tephrosia?) which are sold locally.

Bamboo holds a distinctive place among spontaneous resources. The two species pretum (Dendrocalamus asper) and au (Bambusa vulgaris), which can reach more than 10 cm in diameter and about ten meters in height, have very versatile uses, as container, construction material, sewage .... They are sold 5 US$ per unit for a length of 4 m. Fafulu, another Bambusoideae, is much thinner and is mainly braided to make house walls. The list of used plants, cultivated or not, could be long. Many of them contribute to local people's autonomy and, a central point, to the local economy, either in monetary form on markets or through exchange. These productions and their economic values remain invisible to the public authorities, as the recent census shows (Timor-Leste, 2020), but they gradually enter the tourist market, locally and in Dili (Silva & Ramos de Oliveira, 2020).

Plants and social practices

Under this section, we will briefly discuss the social practices that contribute to the sustainability of biodiversity. An iconic example is given by the palm areca or bua (Areca catechu). Its fruits chewed with lime and betel, malus (Piper betle), have stimulating properties and their use is essential to social well-being. The areca palms are usually planted near the houses or, sometimes, in bunches in specific places, where they are individually owned. One also finds in the area of Makadade areca groves of a 5 . By "spontaneous", we mean plants which presence in a determinate place is not induced by human action or only in an indirect way. Cultivated plants result of a direct intentionality of presence. However cultivated and spontaneous plants are only the two extremities of a gradient of plants management and relationships between a society and their resources. few hectares, on relatively fertile land; they often combine areca and coconut trees, another important economic resource. Each grove is supervised by a guardian. Although the area is used collectively and belongs to a specific clan, each areca bears marks of its individual ownership. In the largest plantation, Abak Tede, every year in July people come from all over the island and also from Dili to take part in the major feast organized for the harvest. This harvest is strictly regulated and any collection of arec nuts before the formal authorization is punishable. On the given day, the guardian distributes grains of maize to the owners according to the number of trees they own. These grains materialize the number of arec nut infrutescences (they are around 10-12 per palm tree) that will have to be given to the guardian of the common grove (this contribution amounts generally to one tenth of the harvest). The guardian will then sell or exchange some of the nuts for tua or dried fish, and some will be kept to be used for the village's social events. The young people who climb the trees to collect the nuts will be paid with one or two of these infrutescences for their hard work. The rest of the production goes to the owner. What is interesting is that the ownership regime of this property combines different statuses depending on whether it refers to land -collective and clan-owned-, to palm trees -individually owned-, or to production that is used in part to remunerate guardians and climbers, in part the owners, and in part is intended for the community.

Another example of collective land status and of private ownership is provided by bamboos, au or pretum, which are not to be felled without permission. The tapping of tua-metan obeys this same pattern and paadu / tarabandu (prohibition mark) frequently mark their stipes. The felling of large trees for timber is submitted to collective authorization. Honey harvesting is another example of natural resource management which combines collective and individual levels. On the slopes of Mount Tutunairana in the southwest of the island, the various clans of Makadade and Maker own customary lands whose resources benefit them alone, especially bani ben, ani eekn, honey from the giant Asian honeybee (Apis dorsata). In these small valleys, the largest trees host every year migrating bee swarms under their branches. These trees, such as nunu (Ficus spp.), are protected and maintained. Once the bee swarms settle, the development of the honeycombs is monitored until the harvest day, a major event where the different lineages of the village get together and meet with their family to cut the combs and share the honey equitably among the participants. This practice contrasts with the individual collection of bani latan, anglatan, which are honey trunks whose harvesting period is less constraint because it depends on the experience and goodwill of their owners (their location, however, should preferably be in a common area, unless they are willing to share the harvested honey with the landowner)6 . Whether plant resources or honey, it is the articulation of individual and collective rights and responsibilities that contributes to the sustainability of natural resources. These resources are managed on a shared basis within the group according to rules that most likely intertwine customary and governmental norms.

Conclusion

The biodiversity present in Ataúro appears to be firmly rooted in a set of technical and social practices according to configurations and dynamics which are not only specific to the island, but also to each group that identifies itself as different from others according to its language, social organization and environment. The approach that we chose focuses on species, ie local or scientific taxonomic entities, but without isolating them from their context; it underlines the diversity of status of these biological resources, from the 'simple use' of a plant, to species or groups of species which have a mythical or historical past, or which organize intra-or inter-group social relations according to customary norms.

Therefore, the reference to the components of biodiversity is collective, affective, dynamic, inherent to the functioning of society and it constitutes a local heritage whose tangible and intangible components are intimately linked.

The tourism development project proposed by the government of East Timor is based on two main elements, biodiversity (marine or terrestrial) and the specificity of local production which integrates new channels of trade. The project capitalizes, as mentioned above, on the knowledge and pratices of local populations on biodiversity, with the risk of requiring them to meet exogenous management standards rather than making them full stakeholders in this project. These standards respond to visions that reduce their modes of action on nature that are part of a continuum to major contrasts such as wild vs. cultivated, forest vs. agricultural, conservation vs. use, laws vs. customary rights, etc., and risk erasing the prominent features that make up the richness of this local heritage and contribute to the material and social well-being of the inhabitants. At the same time, the project is an opportunity to improve livelihoods and to build resilience to climate change, issues that leave no room for nostalgia. Scientific research can be part of this dynamic by developing collaborative approaches that would be more inclusive of young people and women. It could propose instruments, digital in particular, which would allow a multi-scalar approaches to the mosaic of territories that constitutes the island of Ataúro; it could strengthen collective and individual innovation capacities in this new context and propose avenues articulating cultural, environmental and agricultural policies.

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	Bambusa vulgaris	au	Imperata cylindrica	hae
	Bambusoideae	fafulu	Imperata cylindrica	lari
	Bambusoideae	luli	Intsia bijuga	ai-besir
	Barringtonia asiatica	ai-ua	Lantana camara	ilau karuk
	Borassus flabellifer	tua	Leucaena leucocephala	ai-kafé
	Cajanus cajan	tunis	Mangifera indica	haas
	Canarium spp	ai-kiar	Mangifera sp.	ah'ran
	Carica papaya	ai-dila	n.i.	eri
	Ceiba pentandra	ai-lele	n.i.	laraho
	Chromolaena odorata	aper hatu	n.i.	meam
	Coix lacryma-jobi	batar-fatuk	non identifié	i-mera
	Corypha utan	ai-tali	Pachyrhizus erosus	sinkomás
	Dendrocalamus asper	pretum	Pachyrhizus sp.	sinkomás
	Derris ou Tephrosia ?	xx	Phaseoleae	fore
	Dioscorea cf. esculenta	kumbili	Phaseoleae	koto
	Entada sp.	kaleik	Piper betle	malus
	Eucalyptus alba	ai-bubur	Pterocarpus indicus	ai-na
	Ficus cf. variegata	muung	Schleicheria oleosa	ai-dak
	Ficus sp. Lexicon of cited plants ah'ran ai-ata ai-besir ai-bubur ai-dak Ficus spp. Garuga floribunda Gyrocarpus americanus Hibiscus tiliaceus Hibiscus tiliaceus	elas Mangifera sp. Annona squamosa Intsia bijuga Eucalyptus alba Schleicheria oleosa hali ai-heu i-puti ai-kfau haru	Schleicheria oleosa fore Sesbania grandiflora haas Setaria italica Sorghum bicolor hae Tamarindus indica hali Tamarindus indicus	i-leti ai-tururo Phaseoleae Mangifera tora batar-ain-naruk indica Mangifera spp. ai-sukaer Imperata cylindrica Ficus spp. ana'r
	ai-dila	Aegle marmelos	haru	Hibiscus tiliaceus
	ai-dila	Carica papaya	ilau karuk	Lantana camara
	ai-hanek	Alstonia scholaris	i-leti	Schleicheria oleosa
	ai-heu	Garuga floribunda	i-mera	non identifié
	ai-kafé	Leucaena leucocephala	i-puti	Gyrocarpus americanus
	ai-kamii	Aleurites moluccana	kaleik	Entada sp.
	ai-kfau	Hibiscus tiliaceus	koto	Phaseoleae
	ai-kiar	Canarium spp	kumbili	Dioscorea cf. esculenta
	ai-lele	Ceiba pentandra	laraho	n.i.
	ai-na	Pterocarpus indicus	lari	Imperata cylindrica
	ai-sukaer	Tamarindus indica	luli	Bambusoideae
	ai-tali	Corypha utan	malus	Piper betle
	ai-tururo	Sesbania grandiflora	meam	n.i.
	ai-ua	Barringtonia asiatica	muung	Ficus cf. variegata
	ana'r	Tamarindus indicus	pretum	Dendrocalamus asper
	aper hatu	Chromolaena odorata	sinkomás	Pachyrhizus erosus
	au	Bambusa vulgaris	sinkomás	Pachyrhizus sp.
	batar-ain-naruk	Sorghum bicolor	tora	Setaria italica
	batar-fatuk	Coix lacryma-jobi	tua	Borassus flabellifer
	bua	Areca catechu	tua-metan	Arenga pinnata
	elas	Ficus sp.	tunis	Cajanus cajan
	eri	n.i.	n.i.	Derris ou Tephrosia ?
	fafulu	Bambusoideae
	Aegle marmelos	ai-dila	Annona squamosa	ai-ata
	Aleurites moluccana	ai-kamii	Areca catechu	bua
	Alstonia scholaris	ai-hanek	Arenga pinnata	tua-metan

"... sêr um zero na balança económico da Província."(Magalhães, 1916:

24).

Makadade region is ratlungu-speaking. However, we indicate the name of plants in tetum in order to facilitate the reading. The few names in ratlungu are in bold type.

It is not the purpose of this article to discuss the concept of "house" or "clan" to designate the lisan. For the sake of simplification, we will use the term "clan" to refer to lineage groups that recognize a common origin and territoriality, and to "houses" to designate the habitats that correspond to them.

unidentified

For similar examples of honey harvesting and management in the region, seeCésard & Heri, 2015.