Issa O Malam
email: oumarou.malam-issa@orleans.inra.fr

Microbiotic soil crusts in the Sahel of Western Niger and their influence on Soil POROSITY and water dynamics

Keywords: Microbiotic crusts, Cyanobacteria, Exopolysaccharides, Pore geometry, Erosion, Runoff, Water retention, Sahel

Microbiotic soil crusts are common features of the surface of fallow land in Western

Niger. We investigated the interaction between these microbial covers and the porosity and water dynamics of soils at the surface of a Sahelian landscape. The soil pore system was examined by microscopic observations and mercury porosimetry. The soil water retention capacity was measured using a Richard pressure membrane apparatus. Runoff measurements were performed in situ at a one m 2 scale under natural rainfall.

Samples with dense cyanobacterial cover had microbially-originated pores ranging from 0.04 and 50 µm in size. These samples also showed higher total soil porosity and retained two to four times more water than samples with thin microbial cover. These properties are closely related to the hydrophobic nature of cyanobacterial components.

Final runoff values obtained on densely covered surfaces were significantly higher compared to those measured on surfaces with thin microbial cover due to the geometry of the microbially-originated pore system and its functioning.

INTRODUCTION

Microbiotic soil crusts result when communities of extremely drought-resistant microorganisms, dominated by cyanobacteria, colonise the soil surface. These crusts are commonly found in arid environments where the vegetation cover is sparse. In the Sahel of Western Niger (West Africa), microbiotic soil crusts are essential components of fallow land and "tiger bush" ecosystems (landscapes of alternating bands of vegetation and bare ground aligned along the contours; [START_REF] Valentin | Soil and water components of banded vegetation patterns[END_REF][START_REF] Malam Issa | Morphology and microstructure of microbiotic soil crusts on a tiger bush sequence (Niger, Sahel)[END_REF]. They occur as a surficial organo-mineral soil layer, usually associated with physical soil crusts, i.e. soil surfaces with a compacted structure, favourable to runoff and interrill erosion [START_REF] Valentin | Sealing, crusting and hardesetting soils in sahelian agriculture[END_REF][START_REF] Ambouta | Définition et caractérisation des structures de végétation contractée au Sahel : cas de la brousse tigrée de l'ouest nigérien[END_REF]. Field observations showed that microbiotic soil crusts control the development of physical crusting and the subsequent removal of particles. These observations were supported by laboratory studies of soil aggregate stability and micromorphological characteristics, which demonstrated the prominent role played by microbiotic crusts in soil particle aggregation (Malam Issa et al., 1999;2001). Despite the abundant literature, the hydrological processes taking place at the surface of microbiotic soil crusts are far from being well understood [START_REF] Belnap | The potential roles of biological soil crusts in dryland hydrologic cycles[END_REF]. In some cases, lower infiltration rates were observed for soils with microbial cover compared to soils with low levels or no microbial cover [START_REF] Kidron | Two causes of runoff initiation on microbiotic crusts : hydrophobicity and pore clogging[END_REF][START_REF] Eldridge | Infiltration through three contrasting biological soil crusts in patterned landscape in the Negev[END_REF][START_REF] Yair | Effects of biological soil crusts on water redistribution in the Negev desert, Israel: a case study in longitudinal dunes[END_REF][START_REF] Li | Microbiotic soil crust and its effect on vegetation and habitat on artificially stabilised desert dunes in Tengger Desert, North China[END_REF][START_REF] Maestre | Infiltration, penetration resistance and microphytic crust composition in contrasted microsites within a Mediterranean semi-arid steppe[END_REF], while in other circumstances the presence of microbiotic soil crusts led to either positive effects [START_REF] Loope | Influence of a soil microfloral crust on select properties of soils under pinyon-juniper in southeastern Utah[END_REF][START_REF] Belnap | Soil microstructure in soils of the Colorado Plateau: the role of the cyanobacterium Microcoleus vaginatus[END_REF][START_REF] Pérez | Microbiotic crusts in the high equatorial Andes, and their influence on paramo soils[END_REF] or had no effect on water infiltration in soil [START_REF] Eldridge | Soil hydrology is independent of microphytic crust cover: Further evidence from wooded semiarid Australian rangeland[END_REF][START_REF] Williams | Microbiotic crust influence on Unsaturated hydraulic conductivity[END_REF]. More recently, literature reviews from Australia, Israel and North America argued that these discrepancies result from a combination of factors related to methodological approaches, rainfall characteristics, soil factors and the biological composition of crusts [START_REF] Eldridge | Biological soil crusts and water relations in Australia deserts[END_REF][START_REF] Warren | Biological soil crusts and hydrology in North American deserts[END_REF][START_REF] Yair | Effects of biological soil crusts on water redistribution in the Negev desert, Israel: a case study in longitudinal dunes[END_REF]. According to [START_REF] Belnap | The potential roles of biological soil crusts in dryland hydrologic cycles[END_REF], data related to soil bulk density, micro-and macropores and the structure of biological crusts are needed to provide insight into the mechanisms explaining how microbiotic soil crusts affect infiltration and runoff. Soil characteristics, such as porosity, may affect water transit through the soil, depending on the connectivity and the size of pores. However, little information is available in the literature about the porosity system of microbiotic soil crusts, which was quantitatively investigated in only a few cases [START_REF] Verrecchia | Physical properties of the psammophile cryptogamic crust and their consequences to the water regime of sandy soils, north-western Negev desert, Israël[END_REF]. Thus, in the present work we focused on soil porosity, runoff and the water retention capacity of soils with microbiotic crusts in Sahelian environments. The study aimed at highlighting soil hydrological processes at the surface of microbially covered soils in a Sahelian ecosystem. The methodological approach was based on comparisons between microbial soil crusts of varied cover and the horizon beneath these crusts.

Results of in-situ runoff measurements are discussed in light of microscopic investigations and laboratory measurements of soil porosity and water retention capacity.

MATERIALS AND METHODS

The study site

The study site is located near the village of Banizoumbou in the western region of Niger (Sahel), 70 km NE of Niamey, the capital city.

The landscape is composed of three major geomorphic units (Fig. 1;[START_REF] Valentin | Sealing, crusting and hardesetting soils in sahelian agriculture[END_REF][START_REF] Courault | Le bassin versant de Sama Dey : premières observations pédologiques et phyto-écologiques[END_REF]:

-a plateau, formed by Tertiary fluvio-lacustrine deposits ('Continental terminal'; [START_REF] Greigert | Description des formations crétacés et tertiaires du bassin des Iullemmeden (Afrique occidentale)[END_REF], which is dissected into several sections by erosion and has a slight slope with a maximum of one percent ( Fig. 1; [START_REF] Ambouta | Définition et caractérisation des structures de végétation contractée au Sahel : cas de la brousse tigrée de l'ouest nigérien[END_REF]. The plateau vegetation shows a characteristic pattern of alternating densely vegetated bands, comprising small trees and shrubs, and bare soil. The landscape structure is controlled by the downward movement of water and is called 'tiger bush' [START_REF] Ambouta | Contribution à l'édaphologie de la brousse tigrée de l'ouest nigérien[END_REF][START_REF] Cornet | Relations entre la structure spatiale des peuplements végétaux et le bilan hydrique des sols de quelques phytocénoses en zone aride[END_REF][START_REF] Malam Issa | Morphology and microstructure of microbiotic soil crusts on a tiger bush sequence (Niger, Sahel)[END_REF].

-sand dunes formed by Pleistocene stabilised-sand with a mean slope of approximately two to five percent (Fig. 1). These are used for cropping pearl millet and cowpea, and support vegetation areas used for pasture during fallow periods.

-valley systems, formed by aeolian, colluvial and fluvial sands, comprise broad sand plains or sand-filled stream beds with a mean slope of three to five percent (Fig. 1).

These are also used for cropping millet and cowpea.

The climate is typical of the southern Sahel, with a single rainy season lasting, roughly, from May to mid October. Total annual rainfall amounted to 529 mm in 1996 and 534 mm in 1997. These values are slightly below the long-term average of approximately 560 mm (Le [START_REF] Le Barbé | Rainfall climatology of the HAPEX-Sahel region during the years 1950-1990[END_REF].

Runoff was measured during the 1996 rainy season from July 16th to October 12th.

Daily rainfall varied from 0.5 to 69.5 mm (fig. 2a, 13.4 mm in average) and lasted from 93 to 160 minutes. The rainfall intensity recorded within the first minute and after 10 minutes of rain ranged from 64 to 86 mm/h and 37 to 55 mm/h, respectively. In total, 33 events occurred during the 1996 rainy season. Runoff measurements were made for approximately 20 events.

Experimental Field parcels

The experimental parcels were located within the sand dune geomorphic unit (Fig. 1). The textural characteristics of soils in this area are shown in table 1. These consisted of poorly aggregated sandy materials of low organic matter content, which are consequently prone to physical crusting. All the experimental parcels were protected from animal disturbance and human activity. They were cut and treated with preemergent herbicides to prevent plant growth. The parcels were classified into two types depending on the age of fallow and their initial microbial cover: "densely covered" or "thinly covered" surfaces. Densely covered surfaces comprised three parcels of nine m 2 located on an area kept fallow and undisturbed for 3 years (a1, b1, c1; Table 2). The percentage of microbial cover ranged from 75 to 80 % (Table 2). Thinly covered surfaces comprised three similar experimental parcels located on 1-year fallow and supporting early stages of microbial cover (a2, b2, d2; Table 2). Existing crusts (physical and microbial) were mechanically destroyed to obtain an initial stage of crust formation. The initial percentage of microbial cover ranged from 10 to 30 % (Table 2).

In situ measurements

Field experiments entailed observations and visual estimations of soil surface cover, as well as measurements of runoff under natural rainfall. A runoff plot was set up inside each experimental parcel by using a five centimetre high metallic frame. The metallic frame used to isolate the runoff plot included a collector system to catch runoff water and soil particles removed from the area. The collector system was formed by a gutter located at the downslope side of the frame, connected to a tank by a pipe. Runoff was measured by determining the amount of rainfall, with a pluviograph located next to the experimental field, and the volume of water which flowed out of the plots following rainfall events.

The soil surface cover inside the runoff plots was measured using the point-quadrats method. The experimental plots were divided into 100 areas of 0.01 m 2 each. A total of five crust features grouped into microbial or physical types were defined on the basis of visual criteria. Soil surface cover was estimated for the initial surface and at three occasions throughout the rainy season.

Laboratory analyses

Two types of samples were analysed in the laboratory. The first type was a sample of microbial cover obtained by removing the superficial layer (ca. 2-5 mm thick), comprising living microorganisms, with a knife. The second type was devoid of microbial cover and samples were made by collecting soil from the underlying soil horizon of areas with microbial cover, and from the bare surface of recent fallow land.

The water retention capacity, porosity and micromorphological characteristics of the two sample types were investigated. The soil water retention capacity was determined using a Richard pressure membrane apparatus. The samples were submitted to pF 2.5 and 4.2. The water retained was measured by weighing the samples before and after the experiments. Mercury porosimetry experiments were performed with a Micromeritics 9310 porosimeter with an operating pressure between 0.003 and 200

MPa. The surface tension and contact angle between the mercury and the soil material were 4.84 N.m -1 and 130°, respectively. The micromorphological characteristics of dry and wet samples with microbial cover were investigated using a JEOL JSM 6400 SEM and a high resolution Hitachi S-4200 SEM equipped with a Polaron LT 7400 cryopreparation system (Cryo-SEM).

Statistical analyses

Statistical analyses were made using XLSTAT 2006 (ADDINSOFT ™, Paris, France).

In order to compare runoff height and ratio from different plots, an analysis of covariance (ANCOVA) was performed, with runoff as the dependent variable and microbial cover and rainfall as covariates. Multiple comparison tests (Tuckey's HSD) were used to test for significant differences in water retention capacity and porosity obtained for samples with dense and thin microbial cover and bare samples.

RESULTS

In situ observations of soil surface cover

The results of our estimations of the soil surface covered by microbial crusts are shown in Table 2. During the rainy season, for densely covered soils, the area covered by microbial surface crust decreased from its initial value (75-80 %) to final values between 32 and 39 % (Table 2). The percentage of microbial cover on thinly covered parcels also decreased from initial values (10-30 %) to 3-12 % at the beginning, and then 0-8 % at the end of the rainy season (Table 2).

Rainfall and Runoff measurements

Runoff was measured under rainfall intensities ranging from 3.5 to 48.5 mm h -1 . The depth of runoff from the different experimental plots was between 0 and 39 mm (fig. 2b). Values measured at the surface of densely covered plots ranged from 0 to 37 mm (8.3 mm in average) vs. 0 to 39 mm (6.6 mm in average) at the surface of thinly covered plots. Runoff coefficient values ranged from 2 to 95 % (39% in average) at the surface of dense covered plots vs. 0 to 93 % (28% in average) at the surface of thinly covered surfaces. Statistical comparison tests (ANCOVA and Tukey HSD) of the results showed that runoff was significantly higher, at the 95 % confidence interval, on plots with dense microbial cover than on thinly covered plots. No runoff was detected for rainfall below 3.5 mm h -1 . More runoff was produced from both plot types when a greater quantity of rain fell during each rainstorm (fig. 2b). The x-intercepts of runoff and rainfall curves were different for densely covered and thinly covered plots. Values of x-intercepts obtained for the surface of densely covered plots (fig. 2b) were lower than those obtained for thin plots (fig. 2b), which means that runoff was generated earlier at the surface of densely covered plots compared to thinly covered plots.

Water retention capacity measurements

The percentage of water retained by samples with dense microbial cover at pF 2.5 ranged from 12 to 14 % (mean 13 % ± 0.7, table 3). These water retention capacity values were significantly higher, at 95 % confidence intervals, than those of thinly covered samples (mean 7 % ± 0.5). The water retention capacity of samples with dense microbial cover was also significantly higher than that of samples lacking microbial cover, i.e. horizon underlying the crust (3 to 4 %, mean 3 % ± 0.6, table 3). The water retention capacity values at pF 4.2 were not significantly different between samples with or without microbial cover. Water retention values at pF 4.2 ranged from 2 to 4 % (table 3, average 3 % ± 0.7), and 2 to 3 % (table 3, average 2 % ± 0.3) for soils samples with, and without microbial cover, respectively.

Mercury porosimetry

The mean values of total pore volume ranged from 207 to 287 mm 3 g -1 and 212 to 233 mm 3 g -1 for samples with and without microbial cover, respectively (fig. 3). The mean values for total pore volume were significantly higher for samples with dense microbial cover compared to those with thin cover and the horizon underlying the crusts (fig. 3,table 3). No significant difference was observed between thin cover samples and samples from underneath the crust. The pore diameter corresponding to the maximum mercury intrusion was between 8.5 to 15 μm for samples with microbial cover and 27 to 35 μm for samples from the underlying horizons (fig. 3).

The cumulative pore volume curves (cpv) displayed different trends between samples (fig. 3). Mercury entry was continuous into pores between 0.006 and 400 μm in samples with dense microbial cover (fig. 3). On the contrary, samples from soil with thin cover and crust-underlying horizons showed no or very little mercury entry for pores between 0.06 and 10 μm (fig. 3).

Micromorphological observations

The surface of bare samples was composed essentially of rounded quartz grains with rare fine particles, whereas soils with microbial cover showed a superficial network formed by cyanobacterial filaments (F, fig. 4) and extracellular polymer secretions (EPS, fig. 5). The soil pore system and particle organisation differed between samples from soil with dense microbial cover, and samples from thin cover and bare soils. Soil with dense microbial cover showed round-shaped pores up to 50-60 µm in diameter (arrows, fig. 4) and elongated angular-shaped pores with variable diameters (fig. 4), both resulting from the rearrangement of filaments and EPS at the surface. At depth, pores appeared to be caused by cyanobacteria filaments growing in the grain inter-spaces (F, fig. 6a) and gluing these together, as well as causing finer soil particles to adhere together (Mc, fig. 6). Pores in soils with low microbial cover were essentially formed by the spaces between sand particles (V, top part of fig. 6b), partially filled with fine particles (Pl, fig. 6b) and sparse filaments (F, fig. 6b). The profile underlying the crust showed a more porous structure, comprised of tubular and interconnected packing voids partially filled with fine particles, and vesicular and round-shaped pores formed by particle compaction (see bottom part of fig. 6a andb). These pores were similar to those found in bare samples.

The behaviour of the microbial cover upon wetting is illustrated in figures 3a. B.

Cyanobacteria of the genus Nostoc showed a spectacular increase in colony volume during rewetting, when the mean diameter of the colonies grew from 50-100 µm to 150-250 µm. The same behaviour was previously reported for other cyanobacterial strains (Schizotrix), with the mean diameter of individual filaments growing from 10-15 µm to 15-20 µm [START_REF] Défarge | Apports du Cryo-microscope électronique à balayage à émission de champ à l'étude des matières organiques et des relations organo-minérales naturelles. II. Application aux croûtes microbiotiques des sols[END_REF].

DISCUSSION

Micromorphological structure of microbial crusts

Using mercury porosimetry, we observed a significant difference between the pore system of samples with dense microbial cover and samples from soil with either thin cover or from the horizon underlying the crust (fig. 3). Samples with dense microbial cover contained large pore volumes, and mercury entered, gradually and continuously, through pores of 400 to 0.006 μm in size (fig. 3; table 3). In contrast, the extent of mercury entry in samples of soil devoid of microbial cover and soil with thin microbial cover was low and discontinuous between 10 and 0.04 μm (fig. 3; table 3). [START_REF] Verrecchia | Physical properties of the psammophile cryptogamic crust and their consequences to the water regime of sandy soils, north-western Negev desert, Israël[END_REF] reported similar results with mercury porosimetry, and found a higher proportion of small size pores (4 to 40 µm in size) in sandy soils with microbiotic crusts compared to sandy soils without these crusts.

Characterisation of the micromorphology of the samples also suggests that cyanobacterial cover is inducing differences in the soil pore system and soil particle organisation (fig. 4 and5). Soils from thin cover parcels mainly showed elongated and rounded pores that are similar to those found in the sub-crust and bare soils. These pores result from packing of sand and silt particles, infilling by finer particles, compaction due to raindrop impacts and, to some extent, faunal activities and the action of plant roots [START_REF] Valentin | Morphology, genesis and classification of surface crusts in loamy and soils[END_REF][START_REF] Malam Issa | Morphology and microstructure of microbiotic soil crusts on a tiger bush sequence (Niger, Sahel)[END_REF]. These mechanisms likely formed the main pores revealed by mercury porosimetry in soils with thin cover, whose sizes ranged from 100 to 400 µm. On the contrary, soils with dense microbial cover showed additional pores, with elongated and rounded shapes and various diameters, ranging between 0.04 and 50 µm (fig. 4). These pores are caused essentially by bacterial filaments which are interwoven in a superficial network; additional pores are formed by the remaining spaces between adjoining filaments (fig. 4). The occurrence of these pores may be related to the physico-chemical properties of cyanobacterial material, which include polymers of hydrophilic and hydrophobic molecules [START_REF] Stanier | Phototrophic prokaryotes: the cyanobacteria[END_REF][START_REF] Decho | Microbial exopolymer secretions in ocean environments: their role(s) in food webs and marine processes[END_REF][START_REF] Kidron | Two causes of runoff initiation on microbiotic crusts : hydrophobicity and pore clogging[END_REF]. The hydrophilic molecules are polysaccharides, known as adhesive exopolymers that help microbial cells to maintain an association with other cells and the physical environment [START_REF] Decho | Microbial exopolymer secretions in ocean environments: their role(s) in food webs and marine processes[END_REF]. The hydrophobic molecules are glycoproteins and lipopolysaccharides; these increase the adhesive forces between adjoining filaments [START_REF] Kidron | Two causes of runoff initiation on microbiotic crusts : hydrophobicity and pore clogging[END_REF][START_REF] Malam Issa | Role of a microbial cover on structural stability of a sandy soil in Sahelian part of western Niger[END_REF]. Both hydrophilic and hydrophobic components confer adhesive properties to cyanobacterial material; these properties control the ability of filaments to adhere to one another and bind soil particles, and hence affect the soil's spatial organisation. The number of microbial pores appeared to increase with the complexity of the superficial network suggesting that the presence and geometry of the pores observed in the microbiotic soil crusts are directly affected by cynaobacteria derived polysaccharides.

Thus, the difference in pore systems between the two types of soil samples, revealed by mercury porosimetry, reflects the presence of micropores derived from cyanobacteria.

Those pores are expected to play a significant role in the water regime of soils with a dense microbial cover.

Microbial cover affects water retention

We observed that water-holding by soil at field capacity (pF 2.5; table 3) of samples with dense microbial cover is two to four times greater than that of bare soil (13 % vs. 3 % on average; table 3). High resolution Cryo-SEM investigations of rewetted samples suggest that this high water-holding capacity is related to the hygroscopic properties of cyanobacteria polysaccharide material (fig. 5B). The spectacular size increase of cyanobacterial colonies in these samples, compared to dry samples (fig. 5A), is due to water absorption and subsequent swelling of cyanobacterial material [START_REF] Galun | Structural and metabolic diversity of two desert lichen populations[END_REF][START_REF] Campbell | Soil stabilization by prokaryotic desert crust: implications for Precambrian land biota[END_REF][START_REF] Decho | Microbial exopolymer secretions in ocean environments: their role(s) in food webs and marine processes[END_REF][START_REF] Belnap | Soil microstructure in soils of the Colorado Plateau: the role of the cyanobacterium Microcoleus vaginatus[END_REF][START_REF] Verrecchia | Physical properties of the psammophile cryptogamic crust and their consequences to the water regime of sandy soils, north-western Negev desert, Israël[END_REF]. The polysaccharide sheath and extracellular secretions of cyanobacteria have been shown to absorb water in amounts several times their original volume, within a period of time ranging from a few to 30 minutes (Durrell and Shields, 1961;[START_REF] Campbell | Desert crust formation and soil stabilization[END_REF][START_REF] Belnap | Soil microstructure in soils of the Colorado Plateau: the role of the cyanobacterium Microcoleus vaginatus[END_REF][START_REF] Verrecchia | Physical properties of the psammophile cryptogamic crust and their consequences to the water regime of sandy soils, north-western Negev desert, Israël[END_REF][START_REF] Kidron | Rainfall-runoff relationship over encrusted dune surfaces, Nizzana, Western Negev, Israel[END_REF]. Water absorption by swelling polysaccharide material allows cyanobacteria to withstand osmotic and matrix water stress [START_REF] De Winder | The role of water retaining substrata on the photosynthetic response of three drought tolerant phototrophic micro-organisms isolated from a terrestrial habitat[END_REF] and to recovery from drought periods [START_REF] Ernst | Carbohydrate formation in rewetted terrestrial cyanobacteria[END_REF]. This function also has a significant effect on increasing soil moisture and absorption of rainfall.

Microbial cover affects water runoff

The results of runoff measurements showed that, regardless of the type of soil cover, high runoff values were obtained. These results reflect the linear relationship between runoff and rainfall characteristics (fig. 2b; [START_REF] Casenave | A runoff capability classification system based on surface features criteria in semi-arid areas of West Africa[END_REF].

However our results also showed that water runoff is influenced by soil microbial cover; the amount of rainfall necessary for runoff generation on densely covered surfaces was lower than that on surfaces with thin microbial cover (fig. 2b). Final runoff measured on densely covered surfaces was also higher compared to values obtained on surfaces with low microbial cover (fig. 2b).

The difference between the runoff characteristics of the two soil types is due to the difference in micromophological features (the presence of microbial pores; fig. 4) and the behaviour of microbial material upon wetting (fig. 5), i.e. repellence by hydrophobic polymers and water retention by polysaccharides. Hydrophobic polymers, which are abundant in dry soils with microbial cover, are known to prevent quick wetting of microbiotic crusts [START_REF] Kidron | Two causes of runoff initiation on microbiotic crusts : hydrophobicity and pore clogging[END_REF][START_REF] Malam Issa | Role of a microbial cover on structural stability of a sandy soil in Sahelian part of western Niger[END_REF]; their repellent effect ceases when soils become wet [START_REF] Kidron | Two causes of runoff initiation on microbiotic crusts : hydrophobicity and pore clogging[END_REF]. Earlier runoff generation on soils with dense microbial cover is also caused by the repellent effect of hydrophobic polymers at the beginning of rain events.

The polysaccharide material can have two types of behaviour upon wetting: limited swelling allowing water circulation in the microbial pores, or a large degree of swelling which reduces microbial pore size. [START_REF] Mazor | The role of cyanobacterial exopolysaccharides in structuring desert microbial crusts[END_REF] found that high concentrations of polysaccharides in sandy soils reduced the amount of water that penetrated the soil. By comparing microbiotic soil crusts containing different types of polysaccharides, these authors demonstrated that runoff generation at the surface of microbiotic soil crusts is positively correlated with the water holding capacity of polysaccharides. According to [START_REF] Verrecchia | Physical properties of the psammophile cryptogamic crust and their consequences to the water regime of sandy soils, north-western Negev desert, Israël[END_REF], pores between 4 and 40 µm can be blocked when cyanobacterial polysaccharide material absorbs water and swells. The polysaccharide content of samples with a dense microbial cover is 1.5 to 3 times higher than that of samples with low microbial cover [START_REF] Malam Issa | Role of a microbial cover on structural stability of a sandy soil in Sahelian part of western Niger[END_REF]. Our cryo-SEM images show the spectacular increase in the size of cyanobacterial colonies during wetting of microbiotic crusts due to the swelling of polysaccharide material in their mucilage (fig. 5a,b). This increase likely reduces the size of pores formed by the cyanobacteria, and subsequently induces the high amount of runoff found on welldeveloped microbial cover.

The roles of other factors, such as soil texture, in runoff generation on soil with microbial cover, may also be considered. In microbial soil crusts of Western Niger, soil texture is greatly affected by accretion of fine airborne particles which are trapped by cyanobacterial material. Accumulation of these particles, observed in thin soil sections, may also contribute to pore clogging and thus to runoff generation on soil with dense microbial cover.

These results agree with work supporting the positive role of microbial cover in runoff generation [START_REF] Kidron | Two causes of runoff initiation on microbiotic crusts : hydrophobicity and pore clogging[END_REF][START_REF] Eldridge | Infiltration through three contrasting biological soil crusts in patterned landscape in the Negev[END_REF][START_REF] Yair | Effects of biological soil crusts on water redistribution in the Negev desert, Israel: a case study in longitudinal dunes[END_REF]. Soil surfaces with dense microbial cover in the Sahelian environment of Western Niger are thus potential areas which may contribute to capture limited water resources. Nevertheless, further studies are needed to evaluate the potential role of microbial cover in water redistribution in this environment. In particular, the impact of underlying physical crusts should be investigated, this influence could be different depending on the degree of microbial cover.

CONCLUSION

This study provides new data on the impact of microbiotic crusts on soil porosity and water dynamics in a Sahelian environment. Our findings confirm that microbiotic crusts are instrumental in generating high runoff. The results also show that polysaccharides and hydrophobic polymers of cyanobacteria affect the porosity of soil with a dense microbial cover. Runoff generation is under the control of the functioning of microbial pores, which itself is closely related to water holding capacity and the hydrophilic nature of cyanobacterial components. Hydrophobic polymers prevent quick wetting of soils with dense microbial cover, and the swelling of polysaccharide material reduces the effective porosity of soil, leading to early and high levels of runoff being generated on these soils. Thus, microbial soil covers could potentially contribute to form runoff-run-on systems that would help capture the limited water resources in the Sahelian environment of Western Niger. This could be beneficial for plant growth in tiger bush and fallow lands.

FIGURE CAPTIONS Figure 1 :

 CAPTIONS1 FIGURE CAPTIONS

Figure 2a :

 2a Figure 2a: Rainfall events throughout1996.

Figure 2b :

 2b Figure 2b: Relationship between rainfall depth and runoff at the surface of soils with

Figure 3 :

 3 Figure 3: Cumulative pore volume curves for microbiotic crust samples and samples

Figure 4 :

 4 Figure 4: SEM micrographs of the surface of soil covered with a dense microbial layer.

Figure 5 :

 5 Figure 5: Cryo-SEM micrographs of the surface of soil with a dense cover of Nostoc

Figure 6 :

 6 Figure 6: Photomicrographs of thin sections. (A) View of the soil profile with a dense

  Figure

  Figure 5A

Figure 6B

  Figure 6B

Table 1 :

 1 textural characteristics of the studied soil.

		Clay	Fine	Coarse silt	Fine sand	Coarse sand
	Particle-size fraction	0-2 µm	2-20 µm	20-50 µm	50-200 µm 200-2000 µm
	Mean values (%)	4.8	3.6	1.6	28.1	62.2
	Standard errors	0.5	1.1	0.6	4.8	7.6

Table 2 :

 2 Soil surface conditions of the experimental plots: initial and value of microbial cover measured at the beginning, during and at the end of runoff measurements periods.

			Period of observations
		Initial (15/06/96) 16/07/1996 04/09/96 23/10/1996
	Soil with dense microbial cover	80	62	50	35
	Soil with thin microbial cover	14	3	4	5

Table 3 :

 3 Water retention capacity and total pore volume measured by mercury porosimetry of samples with and samples devoid of microbial cover. (Mean values of 2 to 4 replicates).

		pF 2.5	pF 4.2	Total pore volume
		%	%	mm 3 g	-1
	Soil with dense microbial cover	13 ±0.7	3 ±0.7	280 ±10
	Soil with thin microbial cover	7 ±0.5	2 ±0.3	210 ±4
	horizon underlying the crust	3 ±0.6	2 ±0.3	222 ±8

ACKNOWLEDGEMENTS

This study formed part of a research programme in West Africa (Projet Jachère) funded by the EU and IRD (Institut de Recherche pour le Développement). The authors gratefully acknowledge J-L. Rajot, Soumana, Alfari, Aboubacar, Abdoulaye and Moumouni for help with field work, and X. Dorothière, H. Gaillard, A. Genty, C. Le Lay, and A. Richard for their skilled technical assistance. The authors thank G. J. Kidron, Leigh Gebbie and an anonymous reviewer for their constructive suggestions and correction of the manuscript and the English.


Sofiane Guebba

Violaine Guy

Théodore Papadopoulo

Marianne Bruno

Maureen Clerc

Marie-Hélène Soriani

Recent work demonstrates feasibility for ALS patients to communicate via P300 speller [1], but end-user's expectations are not met concerning comfort and ease of use, particularly for patient under heavy pathology [8]. One challenge for daily use [8], [9] is to provide patients with gel-free headsets that are easy to put on and comfortable while providing enough signal quality for accurate P300 classification. Our proposal is to custom design a silicone headset to fit patient's head morphology [5], paying attention on good pressure distribution and hair layer penetration. We will firstly show feasibility of Dry P300Speller with State-of-the-Art amplifier, then analyze electrode impedance variation over time while the headset is worn, and its relation to P300 classification accuracy.

Technology Brain Computer Interface for Autonomy: Patient-adapted ergonomic headset for dry-EEG P300 speller Contact: sofiane.guebba@inria.fr

Challenges & Requirements

System evaluation

Overcome the gap between Wet (Fig. 1) and Dry EEG (Fig. 2)

o Adapted electronics o Compromise between comfort and signal quality [4] o Adapted Impedance threshold (e.g 20kOhm for wet (see Fig. 3))

Ease of use [9] o Easy to put on by a non-expert (<3

Fig

  Fig. 1: Textile commercial headset, wet EEG

Fito

  Extract patient head shape from 3D scan [5] o Being reliable for long time (12 months) o Being worn comfortably during long time recording (weight supported by head <400g) o Classification Accuracy o Speed of Use: Information Transfer Rate (ITR) o Comparison with state-of-the-art system [7] Perspectives Better knowledge of aging process of electrodes Add mechatronic parts to increase efficiency (e.g active PCB for each electrodes) Increase portability by user-centered design o Reduce weight / Become wireless / Upgrade aesthetics & autonomy o Good fit on multiple head with the same process I. Validation of the manufacturing process II. Repeatability of the process III. Feedback Questionnaire -SatisfactionImpedance analysis (1h) for the working mode explicited byFiedler [4], revealed that our prototype stand with a mean impedance of 50 kΩ Ω and a variability of 71.6 kΩ (see Fig.3), with the worst contact being 534 kΩ, still in the 1MΩ range defined by literature.

Fig. 3 :Fig

 3 Fig. 3: 1 hour Impedances Analysis per channel: mean and variability

http://team.inria.fr/athena/


Pierre Bessiere
email: pierre.bessiere@imag.fr

Francis Colas
email: francis.colas@college-de-france.fr

Bayesian Programming: life science modeling and robotics applications

How to use an incomplete and uncertain model of the environment to perceive, infer, decide and act efficiently? This is the challenge both living and artificial cognitive systems have to face.

Logic is by nature unable to deal with this question. The subjectivist approach to probability is an alternative to logic specifically designed to face this challenge.

In this paper we introduce Bayesian Programming, a methodology, a formalism and an inference engine to build and compute probabilistic models. The principles are illustrated with two examples: modeling human perception of structure from motion and playing to train a video game avatar.

1 Probability as an alternative to logic for rational sensory-motor reasoning and decision

The subjectivist approach to probability (often partially improperly called "Bayesian approach") proposes probability theory as an alternative to logic for rational reasoning in presence of incompleteness and uncertainty [START_REF] Jaynes | Probability Theory: the Logic of Science[END_REF].

A radical proposition indeed, as logic is the founding paradigm of mathematic, of the scientific methodology, of computer science and technology and, possibly, the only common denominator of the different theories of brain and cognition.

The rationale for this proposition is that both living creatures and artificial cognitive systems have to face the same fundamental difficulty: how to use an incomplete and uncertain model of their environment to perceive, infer, decide and act efficiently? Indeed, any model of a real phenomenon is incomplete. Hidden variables, not taken into account in the model, influence the phenomenon. The effect of these hidden variables is that the model and the phenomenon never behave exactly alike. Uncertainty is the direct and unavoidable consequence of incompleteness. No model may foresee exactly the future observations of a phenomenon, as these observations are biased by the hidden variables. No model may either predict exactly the consequences of its decisions.

The subjectivist approach deals with incompleteness and uncertainty with a two steps process: learning and inference (see Figure 1). Learning: Learning transforms the irreducible incompleteness into quantified uncertainty (i.e. probability distributions). These distributions result from both the preliminary knowledge of the reasoning subject and the experimental data coming from the observation of the phenomenon.

The preliminary knowledge, even imperfect and incomplete, is relevant and provides interesting hints about the observed phenomenon. It is not a fixed and rigid model purporting completeness but a gauge, with free parameters, waiting to be molded by the experimental data.

The experimental data obtained from the physical interaction with the environment reflects all the complexity of this interaction. This includes the effect of the hidden variables that are not taken into account by the preliminary knowledge. Learning sets the values of the free parameters of the preliminary knowledge using the experimental data. Thus, the influence of the hidden variables is taken into account and quantified.

The more accurate and pertinent (i.e. the less incomplete) the preliminary knowledge is, the less uncertain and the more informational the learned distributions are. Inference: Inference is performed with the probability distributions obtained by the first step. To do so, we only require the two basic rules of Bayesian inference (Bayes theorem and the normalization rule). These two rules are to Bayesian inference what the resolution principle is to logical reasoning [START_REF] Robinson | Logic: Form and Function[END_REF], they are sufficient to perform any inference on discrete probability distributions. These inferences may be as complex and subtle as those achieved with logical inference tools. Indeed, it can be shown that logical inference is a particular case of probabilistic inference [START_REF] Jaynes | Probability Theory: the Logic of Science[END_REF].

Bayesian Programming formalism and automation

The necessary information to completely specify a probabilistic model is made of the relevant variables, the conditional dependencies between these variables, the parametric forms of the associated probability distributions and the values of these forms' parameters.

Such models are usually presented with different graphic forms (Bayesian Networks by [START_REF] Pearl | Probabilistic reasoning in Intelligent Systems: Networks of Plausible Inference[END_REF] or graphical models by [START_REF] Frey | Graphical Models for Machine Learning and Digital Communication[END_REF]). The relevant variables are nodes, their conditional dependencies are vertices between these nodes, and the parametric forms are associated to each node. As probability is an alternative to logic, it is also possible to use an algebraic formalism to define the probabilistic models. We proposed the Bayesian Programming formalism to do so [START_REF] Lebeltel | Bayesian robot programming[END_REF].

A Bayesian program (BP) is made of two parts:

• a description that is the probabilistic model of the studied phenomenon or the programmed behaviour; and • a question that specifies an inference problem to solve using this model.

A description itself contains two parts:

• a specification part that formalizes the knowledge of the programmer; and • an identification part in which the free parameters are learned from experimental data.

Finally, the specification is constructed from three parts:

• the selection of relevant variables to model the phenomenon;

• a decomposition, whereby the joint distribution on the relevant variables is expressed as a product of simpler distributions exploiting conditional independence between variables; and • the parametric forms in which either a given mathematical function or a question to another BP is associated with each of the distributions appearing in the decomposition.

Two examples of a Bayesian Program (see figures 2 and 6) are given in the next sections, where the methodology to build them is also explained.

Furthermore, we developed ProBT R3 a C++ API which given a BP automate all the necessary computation to get the probability distribution answering the question.

Perception of structure from motion

Perception is often stated as the inverse problem of infering properties on the environment starting from sensations given by the senses and some uncertain rules of what should the sensations be for a given state of the environment. The perception of three-dimensional structure from motion (SFM) is one such example that has been studied [Helmholtz, 1867, Wallach and[START_REF] Wallach | The kinetic depth effect[END_REF]. However SFM is ill-posed as an infinite number of combinations of geometry and motion can lead to the same optic flow. The first hypothesis introduced to reduce this ambiguity is that the optic flow is produced by a rigid object in motion [START_REF] Ullman | The interpretation of visual motion[END_REF][START_REF] Koenderik | Optic flow[END_REF]. However recent experiments have shown that the same optic flow could be interpreted differently depending on the motion of the observer. This lead to the proposal of the stationarity hypothesis, which states that the motion of the object is probably small in the allocentric reference frame [START_REF] Wexler | The stationarity hypothesis: an allocentric criterion in visual perception[END_REF][START_REF] Wexler | Voluntary head movement and allocentric perception of space[END_REF].

Bayesian model

In this section, we take the example of the perception of a moving planar surface. This general set-up involves a monocular participant placed in front of a monitor in the dark. The stimulus is a set of light points on a dark background depicting a planar patch with a random-dot texture. The participants stare at a fixation cross and the movement of the head of the participants are recorded so as to control the optic flow presented. The task consists in reporting the configuration of the plane by aligning a grid presented on the screen to the mean configuration of the plane perceived.

We define a Bayesian model of an observer submitted to this experiment. It takes as input the optic flow and the self-motion of the observer, and delivers a judgement on the plane configuration. This model is based on the following three hypotheses:

• (H1) rigidity: the optic flow perceived is probably caused by a rigid object in relative motion, • (H2) stationarity: the movement of this object is probably small, • (H3) independence between the configuration of the object, the motion of the object and the motion of the observer.

The first two hypotheses are justified in the literature whereas the third one is a common assumption made explicit in our model.

Variables: Within the Bayesian Programming formalism, the first step in the definition of a model is the choice of the relevant variables. This choice is done according to the aim of the model and the hypotheses involved.

In our case, we wish to extract the configuration of a plane from the observation of the optic flow. Therefore we have at least a variable Θ to represent the configuration and a variable Φ to represent the optic flow. More precisely, Θ will be the tilt angle of the plane; that is, the angle between the vertical and the intersection between the object plane and the frontoparallel plane. The optic flow Φ will be parametrized by the Taylor series of the velocity field of the projected dots (see [START_REF] Longuet | The visual ambiguity of a moving plane[END_REF]).

The model has to take into account the self-motion of the observer. This is represented with the variable M that is the 3D-vector of translation of the observer in an allocentric reference frame.

Finally, the rigidity hypothesis H1 involves the relative motion of the plane with respect to the observer and hypothesis H2 involves the absolute motion of the plane with respect to an allocentric reference frame. Thus, we consider respectively the variables X R and X A for both the relative and absolute motion of the plane.

Decomposition In order to specify the joint distribution, we use the conditional independencies implied by our hypotheses.

Hypothesis (H1) states that the optic flow does not depend on anything else than the object and its relative motion with respect to the observer. This writes:

P (Φ | Θ M X R X A ) = P (Φ | Θ X R ) (1)
On the other hand, hypothesis (H3) states that the configuration of the object, the motion of the object and the motion of the observer are independent. This writes:

P (Θ M X R X A ) = P (Θ)P (M)P (X A )P (X R | M X A ) (2)
Using Bayes' rule on the joint distribution over all the variables of our model, we write the decomposition:

P (Φ Θ M X R X A ) = P (Θ)P (M)P (X A )P (X R | M X A )P (Φ | Θ X R ) (3)
Parametric forms: The decomposition involves five factors that we have to specify in order to complete the joint distribution over all the variables of the model:

• P (Θ): as none of our hypotheses involves this prior, we use the maximum entropy distribution which yields a uniform distribution over the angle Θ; • P (M): this factor is not used in the inference (see expression 5) and can be left unspecified; • P (X A ): the stationarity hypothesis (H2) states that the absolute motion is more probably small, thus this distribution is chosen as a Gaussian distribution with the null vectors as mean and a given covariance matrix. • P (X R | M X A ): this factor expresses the reference frame change between absolute and relative motion. More precisely, this is a Dirac distribution on the exact relative motion computed from the given motion of the observer and absolute motion of the object: x R (M, X A ). • P (Φ | Θ X R ): the rigidity hypothesis (H1) states that the optic flow is probably due to a rigid object. Therefore we specify this factor as a Gaussian distribution, centered on the theoretical optic flow for a plane in this given configuration Θ and for this given relative motion X R . The covariance matrix states how much we expect the flow to differ from a rigid one.

Question and inference: The task of the observer is evaluate the configuration of the plane given the optic flow and its own motion. In probabilistic terms, this means computing:

P (Θ | φ m) (4)
With the joint distribution over all our variables, standard Bayesian inference yields the following expression to answer this question:

P (Θ | φ m) ∝ P (Θ) xA P (x A )P (φ | Θ x R (m, x A )) ( 5
)
The model is summarized in figure 2.

Program 8 > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > : Description 8 > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > : Specification 8 > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > :
Relevant Variables: Φ, Θ, M, XR, and XA Decomposition:

P (Φ Θ M XR XA) = P (

Results: stationarity and rigidity

To validate the model, we compared its results with experimental results from six different psychophysical experiments [START_REF] Colas | A unified probabilistic model of the perception of three-dimensional structure from optic flow[END_REF]. Here, we present the example of a conflict between both the rigidity and stationarity hypothesis.

Description of the experiment: The experimental results are taken from [START_REF] Wexler | The stationarity hypothesis: an allocentric criterion in visual perception[END_REF]. The aim is to investigate the relative importance of both stationarity and rigidity by presenting stimuli with two main interpretations: one more rigid and a second more stationary.

More precisely, the optic flow of a rotating plane can be similar to a the optic flow of a plane in another orientation with both a relative translation and rotation (see figure 3). When the optic flow of the first plane is presented, the second can sometimes be perceived, even if this alternative solution is less rigid (not exactly the same optic flow) and less stationary (one translation and one rotation compared to only the rotation). However, if the observer is in translation in the opposite direction, the relative translation of the object in the alternative solution and the translation of the observer can cancel out the translation of the object in the absolute reference frame. In this case, the alternative is still less rigid than the original solution but is more stationary. In this experiment, the observer is asked either not to move the head, called immobile condition, or to move the head in a sagittal translation, called active condition. The simulated plane can either be in relative translation with respect to the observer, condition A, or at a fixed distance, condition B. Immobile/active and condition A and B are crossed to produce the four experimental conditions sumarized in figure 3. The velocity of the plane is set according to the motion of the observer so that the orientations of both simulated and alternative planes are orthogonal. In the four conditions, the alternative solution is less rigid than the simulated plane, but in conditions A-immobile and B-active, the alternative solution is more stationary.

The task for the observer is still to judge the orientation of the plane. The responses are said non-rigid if the orientation reported is nearer the alternative solution than the simulated solution.

The left graph in figure 4 shows the fraction of non-rigid responses for each four experimental conditions. We can see that in conditions A-immobile and B-active, the percentage of non-rigid responses is greater than 50%.

Model analysis: The right graph in figure 4 shows the results of the model in the same four conditions. We can see that, in accordance with the experimental results, the probability of non-rigid response is greater than 50% in both conditions A-immobile and B-active and smaller than 50% in conditions Bimmobile and A-active.

This result is explained by the product between the prior on the absolute motion and the probability of the presented optic flow given the orientation and the relative motion. For the alternative response, the value of P (φ | Θ X R )

Experimental results

Model results is smaller than for rigid response. However, this is compensated for by a larger probability of the absolute motion P (X A ).

This example shows that a Bayesian model can reproduce results from psychophysical experiments.

Playing to train your video game avatar

Today's video games feature synthetic characters involved in complex interactions with human players. A synthetic character may have one of many different roles: a tactical enemy, a partner for the human, a strategic opponent, a simple unit among many, or a substitute for the player.

In all of these cases, the game developer's ultimate objective is for the synthetic character to act as if it were controlled by a human player. This implies the illusion of spatial reasoning, memory, common-sense reasoning, using goals, tactics, planning, communication and coordination, adaptation, unpredictability... In current commercial games, basic gesture and motion behaviours are generally satisfactory. More complex behaviours usually look much less lifelike. Sequencing elementary behaviours is a difficult problem, as compromises must be made between too-systematic ordering that always appears as an automaton and too-hectic behaviour that looks ridiculous.

We address this problem of real-time reactive selection of elementary behaviours for an agent playing a first-person shooter (FPS) game called Unreal Tournament. In this kind of game, a group of people play together via the Internet. Each of them can control a virtual avatar. This avatar may act and navigate in a virtual 3D environment. It may also interact with the avatars of other players or with autonomous characters called bots controlled by a program. In FPS games, the main interaction with the other players and bots consists of trying to slaughter them while surviving as long as possible.

The goal of this work is to demonstrate how, by using the Bayesian inverse programming technique, a player of a video game can teach an avatar how to play autonomously (see Fig. 5).

Bayesian model

Variables: Six elementary reactive behaviours have been programmed based on these actions: attack foes (attack), search for weapon bonuses (searchweapon), search for health bonuses (searchhealth), explore the environment (explore), flee (f lee), and detect danger (detectdanger). The goal of the program is to decide every tenth of a second which of these 6 behaviors should be applied. The game provide 7 "sensory" pieces of information to do so. Consequently, the relevant variables are as follows:

• B t , the reactive behaviour of the bot at time t, which can take any of the six values: {attack, searchweapon, searchhealth, explore, f lee, detectdanger}. • H t , the bot's health level at time t. • W t , the weapon that the bot is deploying at time t. • OW t , the opponent's weapon at time t.

• N t , a Boolean variable indicating whether a noise has been heard recently.

• N O t , the number of close enemies at time t.

• W P t , the proximity of a weapon bonus.

• HP t , the proximity of a health bonus.

Each of these 8 variables has to be considered for each instant between time 0 and T . This leads to a conjunction of 8 × (T + 1) variables4 : B 0:t ∧ . . . ∧ HP 0:t . Decomposition: Usually, bots' behaviour in video games are specified using a scripting language with a set of rules use to sequence the activation of elementary reactive behaviours. Each rule is a list of conditions and constraints on the sensory variables that have to be verified to select the corresponding reactive behaviour. The generic form of such a rule is: if condition 1 and condition 2 and . . . and condition n then reactivebehaviour i .

There are 2 main ideas in inverse programming:

1. The first one is that knowing which reactive behaviour the robot is doing provides a lot of information on its' sensory variables. 2. The second is that knowing the reactive behaviour we can consider, as a first approximation, that these sensory variables are independent from one another.

Consequently, the rules are replaced by probability distributions expressing chunk of knowledge of the form if reactivebehaviour i then (approximately) condition j . This is why it is called inverse programming.

The joint distribution is decomposed as follows.

P (B 0:t ∧ H 0:t ∧ W 0:t ∧ OW 0:t ∧ N 0:t ∧ N O 0:t ∧ W P 0:t ∧ HP 0:t ) = T t=1

P (B t | B t-1 ) ×P (H t | B t )×P (W t | B t )×P (OW t | B t )×P (N t | B t ) ×P (N O t | B t )×P (W P t | B t )×P (HP t | B t ) ×P (B 0 ∧ H 0 ∧ W 0 ∧ OW 0 ∧ N 0 ∧ N O 0 ∧ W P 0 ∧ HP 0 ) (6)
In this decomposition, we assume that:

• The behaviour B t at time t depends on the behaviour B t-1 at time t -1;

• The seven sensory variables may be considered to be independent of one another and independent of the past, knowing the behaviour B t .

This decomposition is similar to the naive Bayes sensor fusion schem. The difference is that the fusion is usually done on some phenomenon whereas in our case the aim is an appropriate action to be executed.

Parametric forms:

The eight terms of the decomposition P (B t | B t-1 ) • • • P (HP t | B t ) are defined using tables specifying their discrete values. For instance, P (H t | B t ), defined in Table 1, gives the probability distribution for H t (the bot's health level), knowing the behaviour B t . We read the first column this way: given that the bot is in state attack, we state that it has a very low probability (10 -3 ) of having a low (poor) health level, a medium probability (10 -1 ) of having a medium (fair) health level, and a strong probability (0.899) of having a high (good) health level.

attack searchweapon searchhealth explore f lee detectdanger Low 10 -3 10 -1 x 10 -1 0.7 10 -1 Medium 10 Learning: The value of these 8 tables may be either specified by the game designer (as in the example of Table 1) or, more interestingly, learned by observing a player.

The difficulty to learn this table from the data recorded by observing the player is that the only observable variables are the 7 sensory ones. The behavior selected by the player is not known (the value of B t is missing). The very well known Baum-Welch [START_REF] Baum | An inequality and associated maximization technique in statistical estimation for probabilistic functions of markov processes[END_REF][START_REF] Rabiner | A tutorial on hidden markov models and selected applications inspeech recognition[END_REF]] algorithm, a special case of the Expectation-Maximisation (EM) class of algorithms [START_REF] Dempster | Maximum likelihood from incomplete data via the em algorithm[END_REF], has been designed especially for learning when some data are missing. We apply an incremental version of the Baum-Welch algorithm as described by [START_REF] Florez-Larrahondo | Incremental learning of discrete Hidden Markov Models[END_REF]. In this algorithm, contrary to the classical Baum-Welch algorithm, the model parameters are re-estimated after each new observation. This algorithm can treat at least 10 sensori-motor acquisition by second allowing to do the learning on line as the player is using the game.

Question and inference: When playing autonomously, every tenth of a second, our bot must make a decision on its behaviour. It must answer the following probabilistic question:

P (B t | b t-1 ∧ h t ∧ w t ∧ ow t ∧ n t ∧ no t ∧ wp t ∧ hp t ) (7)
What is the probability distribution on behaviour at time t (B t ) knowing the behaviour at time t-1 (b t-1 ) and knowing all the sensory information at time t (h t , . . . , hp t )? This question leads to a probability distribution, from which we draw a value to decide the actual new behaviour. The answer to this question may be easily computed as it is proportional to the product of the individual terms:

P (B t | b t-1 ∧ h t ∧ w t ∧ ow t ∧ n t ∧ no t ∧ wp t ∧ hp t ) ∝ P (B t | b t-1 ) × P (h t | B t ) × P (w t | B t ) × P (ow t | B t ) ×P (n t | B t ) × P (no t | B t ) × P (wp t | B t ) × P (hp t | B t ) (8)
Bayesian Program: The corresponding Bayesian program summarizing all this is then given by Fig. 6.

Results

The bots obtained this way after 15 minutes of online learning were faced to other bots or humans in tournaments. For instance, we collected data on series of ten tournaments with the native bots of the game (the one used in the commercial game to fight the human players). Our trained bots compare well with these bots, with skills corresponding to an average human player (see Table 2).

A much more detail description of this work and analysis of the obtained results may be found in Ronan Le Hy's PhD dissertation and publications [START_REF] Hy | Programmation Bayésienne de Personnages de Jeux Vidéos[END_REF][START_REF] Hy | Teaching bayesian behaviors to video game characters[END_REF]

] Program 8 > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > : Description 8 > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > : Specification 8 > > > > > > > > > > > > < > > > > > > > > > > > > :
Relevant Variables: B 0:t , H 0:t , W 0:t , OW 0:t , N 0:t , N O 0:t , W P 0:t and HP 0:t Decomposition: P (B 0:t ∧ H 0:t ∧ W 0:t ∧ OW 0:t ∧ N 0:t ∧ N O 0:t ∧ W P 0:t ∧ HP 0:t ) =

Q T t=1 » P (B t | B t-

Conclusion

Numerous other models and robotics applications have been developed using the Bayesian Programming approach and the API ProBT R . Indeed, 14 PhD theses have been defended in different European Universities using this approach and formalism. Beside the 2 already presented subjects these theses cover the following fields: Bayesian Robots Programming [START_REF] Lebeltel | Bayesian robot programming[END_REF], Bayesian navigation on sensory-motor trajectories [START_REF] Pradalier | The cycab: a car-like robot navigating autonomously and safely among pedestrians[END_REF], Bayesian occupancy filters [START_REF] Coué | Bayesian occupency filtering for multi-target tracking[END_REF], Topological SLAM [START_REF] Tapus | Topological SLAM -Simultaneous Localization and Mapping with Fingerprints of Places[END_REF]], Bayesian CAD system [START_REF] Mekhnacha | The design and implementation of a bayesian CAD modeler for robotic applications[END_REF], Computer-assisted surgery for total hip replacement (THR) [START_REF] Amavizca-Ruiz | 3D human hip volume reconstruction with incomplete multimodal medical images[END_REF], Probabilistic robotics arm control [START_REF] Garcia-Ramez | Programmation bayésienne des bras manipulateur[END_REF], Probabilistic contextual situation analysis [START_REF] Ramel | Multi-modal interaction using bayesian network to manage ambiguous situations[END_REF], Bayesian maps [START_REF] Diard | Merging probabilistic models of navigation: the bayesian map and the superposition operator[END_REF], Bayesian approach to action selection and attention focusing [START_REF] Koike | Bayesian Approach to Action Selection and Attention Focusing[END_REF], Bayesian modelling of visual-vestibular interactions [START_REF] Laurens | Bayesian processing of vestibular information[END_REF], Early speech acquisition [START_REF] Serkhane | Building a talking baby robot[END_REF]. These works prove the generality of the approach and the power of expression of the formalism. For more information and up to date panorama of on going developments please refer to Bayesian Programming site (www.bayesian-programming.org).

Fig. 1 .

 1 Fig. 1. The subjectivist approach to incompleteness

Fig. 2 .

 2 Fig. 2. Bayesian model of shape perception from motion

Fig. 3 .

 3 Fig. 3. Summary of experimental conditions. The optic flow is exactly the same for conditions A-active and A-passive, and for conditions B-active and B-passive.

Fig. 4 .

 4 Fig. 4. Comparison of the model results with the experimental results.

Fig. 5 .

 5 Fig. 5. Playing Unreal Tournament to train your avatar

Table 1 .

 1 P (H t | B t )

		-1	x	10 -2	x	0.2	x
	High	x	x	10 -3	x	0.1	x

Table 2 .

 2 1 ) ×P (H t | B t )×P (W t | B t )×P (OW t | B t )×P (N t | B t ) ×P (NO t | B t )×P (W P t | B t )×P (HP t | B t ) -×P (B 0 ∧ H 0 ∧ W 0 ∧ OW 0 ∧ N 0 ∧ N O 0 ∧ W P 0 ∧ HP 0 ) Parametric Forms:All distributions are tables. Identification:In real time observing a player Question:P (B t | b t-1 ∧ h t ∧ w t ∧ ow t ∧ n t ∧ no t ∧ wp t ∧ hp t )Fig.6. Sequencing a bot's reactive behaviours by inverse programming Performance comparison (3). Lower is better: minimum 0, maximum 100.

	Behaviour	Score
	Random behaviour	43.2
	Unreal Tournament bot (3/8) (≃ average human) 11.0
	Incremental Baum-Welsh	8.5

This API is available as a commercial product from the ProBAYES company (www.probayes.com) and for free for research and teaching purposes on the Bayesian-Programming.org site (www.bayesian-programming.org).

The notation B 0:t stands for the conjunction of T + 1 variables:B 0 ∧ B 1 ∧ . . . ∧ B T


Michel Olvera
email: michel.olvera@inria.fr

Emmanuel Vincent

Gilles Gasso

Improving Sound Event Detection with Auxiliary Foreground-Background Classification and Domain Adaptation

Keywords: Sound event detection, foreground-background classification, semi-supervised learning, domain adaptation

published or not. The documents may come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Over the past five years, the interest in environmental acoustic scenes has increased considerably among researchers in the field of audio signal processing, largely driven by the Detection and Classification of Acoustic Scenes and Events (DCASE) Challenge and Workshop series [START_REF] Plumbley | Proceedings of the Detection and Classification of Acoustic Scenes and Events 2018 Workshop[END_REF][START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF][START_REF] Ono | Proceedings of the Fifth Workshop on Detection and Classification of Acoustic Scenes and Events[END_REF]. As a result, many tasks involving the automatic analysis of ambient sounds have progressed substantially. This includes sound event detection (SED), a core task for home surveillance or assisted living [START_REF] Van Hengel | Audio event detection for in-home care[END_REF][START_REF] Alsina-Pagès | homesound: Real-time audio event detection based on high performance computing for behaviour and surveillance remote monitoring[END_REF][START_REF] Debes | Monitoring activities of daily living in smart homes: Understanding human behavior[END_REF].

To this end, DCASE Challenge Task 4 encourages the development of methods that contribute to the advancement of SED methods that are trained in a semi-supervised way with a heterogeneous dataset [START_REF] Turpault | Training sound event detection on a heterogeneous dataset[END_REF] including a set of synthetic soundscapes with annotations indicating the sound events class labels and timestamps (strong labels), as well as a set of real recordings, mostly unlabeled and where only a small subset contains at most information about the active sound classes in the recordings (weak labels). The objective of the task is to find for a given soundscape the class of This work was made with the support of the French National Research Agency, in the framework of the project LEAUDS "Learning to understand audio scenes" (ANR-18-CE23-0020). Experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations (https://www.grid5000.fr).

the active sounds as well as their onset and offset time. Many improvements to the Task 4 baseline system have been proposed: augmentation schemes to improve generalization [START_REF] Li | Semi-supervised sound event detection using random augmentation and consistency regularization[END_REF][START_REF] Miyazaki | Conformer-based sound event detection with semi-supervised learning and data augmentation[END_REF]; changes in the acoustic front-end with alternative time-frequency representations to log-Mel spectrograms [START_REF] Copiaco | A study of features and deep neural network architectures and hyperparameters for domestic audio classification[END_REF] or time-frequency resolutions for each sound event class [START_REF] De Benito-Gorron | A multi-resolution approach to sound event detection in dcase 2020 task4[END_REF]; modifications to the backbone architecture with appended multi-task branches and post-processing techniques to refine the outputs [START_REF] Huang | Guided multi-branch learning systems for sound event detection with sound separation[END_REF][START_REF] Cances | Multi task learning and post processing optimization for sound event detection[END_REF][START_REF] Cornell | Domain-adversarial training and trainable parallel front-end for the dcase 2020 task 4 sound event detection challenge[END_REF].

In this work we propose two methods to improve SED in domestic environments. First, we propose the classification of sounds by their spectro-temporal content as foreground or background events as an auxiliary task for SED. This broad categorization of sound events was shown to be useful for deep neural network-based source separation systems to differentiate rapidly varying spectro-temporal features of short duration sound events from slowly varying features of long duration sounds [START_REF] Olvera | Foregroundbackground ambient sound scene separation[END_REF][START_REF] Varma | Learning to separate: Soundscape classification using foreground and background[END_REF]. The proposed foreground-background classifier is jointly trained with the SED branch in a multi-task fashion and the combination of both branches is also investigated. The second improvement is a domain adaptation strategy to reduce the mismatch between synthetic and real recordings. Our proposed strategy aligns the empirical distributions of the feature representations of active and inactive frames of synthetic and real data via optimal transport [START_REF] Courty | Joint distribution optimal transportation for domain adaptation[END_REF][START_REF] Damodaran | Deepjdot: Deep joint distribution optimal transport for unsupervised domain adaptation[END_REF]. Altogether the proposed methods lead to enhanced performance in terms of the event-based macro F1-score on the Domestic Environment Sound Event Detection Dataset (DESED) validation and public evaluation sets [START_REF] Turpault | Sound event detection in domestic environments with weakly labeled data and soundscape synthesis[END_REF][START_REF] Serizel | Sound event detection in synthetic domestic environments[END_REF].

The remainder of this article is organized as follows. In Section 2 we present the proposed improvements to the SED task. Experimental evaluation is discussed in Section 3 and lastly, we conclude the paper in Section 4.

PROPOSED METHODS

Foreground-background classification

Let X , Y and Z be the input, output and latent space. For the SED task we denote the soundscape time-frequency representation by x ∈ X with corresponding annotations y ∈ Y. We have access to a synthetic dataset with strong labels D S = {(x s i , y s i )} ns i=1 and two datasets of real recordings: a weakly labeled dataset D W = {(x w i , y w i )} nw i=1 and an unlabeled dataset D U = {x u i } nu i=1 . The SED model is a Mean Teacher model [START_REF] Tarvainen | Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results[END_REF] in which both the student and the teacher models have the same convolutionalrecurrent neural network (CRNN) architecture. We use the CRNN from the student model as a representation mapping g : X → Z, where the log-Mel spectrograms are mapped to the latent space. The SED model is represented by the function f : Z → Y that maps the latent representations to the output space.

FB branch

Motivated by the broad categorization of sound events into foreground and background according to their spectro-temporal structure, we propose a foreground-background (FB) auxiliary classifier fFB : Z → Y FB that maps the latent space to foregroundbackground labels. We learn this classifier jointly with the SED model in a multi-task fashion, hypothesizing that these different yet related classification tasks will help improve the network's generalization capability. Analogously, for the teacher model we denote by g , f and f FB , the CRNN embedding function, SED and FB branches, respectively. Figure 1 shows the proposed system depicting the student model.

To train the FB classifier in the multi-task paradigm, we derived foreground-background ground-truth annotations y fb i from the strong labels y s i of the synthetic data by combining the sound event labels in two categories: foreground: (alarm -bell ringing, speech, cat, dog, dishes) and background (blender, vacuum cleaner, frying, electric shaver -toothbrush, running water). The SED model is optimized by minimizing

LSED = L(y s i , f (g(x s i ))) + λLstrong(f (g(xi)), f (g (xi)))+ L(y w i , f (g(x w i ))) + λLweak(f (g(xi)), f (g (xi)))+ L(y fb i , fFB(g(x s i ))) + λLstrong(fFB(g(xi)), f FB (g (xi))) (1)
where L(•, •) is a binary cross-entropy classification loss, and Lstrong(•, •) and Lweak(•, •) are mean-square error consistency costs which are differentiable on their second parameter over strong (frame-level) and weak (clip-level) scores, respectively. The consistency weight λ is tied to all consistency costs.

SEDFB branch

Going beyond the proposed FB classification branch, we explored its fusion with the SED branch into a detection branch (SEDFB) to refine outputs. This branch is represented by a function fSEDFB :

Y × Y FB → Y (f SEDFB
LSEDFB =L(y s i , fSEDFB(w s i )) + λLstrong(fSEDFB(wi), f SEDFB (wi)). (2)
The overall cost involving the SEDFB branch is given by

L = LSED + LSEDFB. (3)

Output smoothing

We used two methods to post-process the SED frame-level scores.

The first method corresponds to smoothing the binary multi-label frame-level scores with a median filter of 0.45 s. The second approach consists of Hidden Markov Model (HMM) decoding. Following the same procedure as in [START_REF] Cornell | Domain-adversarial training and trainable parallel front-end for the dcase 2020 task 4 sound event detection challenge[END_REF], we determined the optimal transition probabilities for each sound event class using the validation set. We contrast the contribution of both post-processing schemes in Section 3.3.

Domain adaptation for sound event detection

From the unsupervised domain adaptation perspective, we regard the synthetic dataset with strong labels as the source domain S = D S , and the combination of real recordings from the weakly and unlabeled dataset as the target domain T = D W ∪ D U . We denote as x s and x t the soundscapes from S and T , respectively. In contrast to adversarial adaptation approaches that introduce a domain discriminator to reduce the distribution discrepancy between domains [START_REF] Cornell | Domain-adversarial training and trainable parallel front-end for the dcase 2020 task 4 sound event detection challenge[END_REF][START_REF] Yang | Two-stage domain adaptation for sound event detection[END_REF][START_REF] Park | Weakly labeled sound event detection using tri-training and adversarial learning[END_REF], our proposed strategy relies on optimal transport for its ability to find correspondences between samples by exploiting the geometry of the underlying space. We adopt the DeepJDOT framework [START_REF] Damodaran | Deepjdot: Deep joint distribution optimal transport for unsupervised domain adaptation[END_REF], to correct the mismatch between the distributions of learned feature representations in the two domains.

Joint distribution optimal transport

Let µs = ns i=1 aiδ g(x s i ),y s i and µt = nt i=1 biδ g(x t i ),y t i be two empirical distributions on the product space Z × Y, where δ g(x i ),y i is the Dirac function at position (g(xi), yi) ∈ Z × Y, and ai and bi are uniform probability weights, i.e. ns i=1 ai = nt i=1 bi = 1. The associated cost for the i-th source and j-th target element can be expressed as a weighted combination of costs in the latent and label spaces d(g(x s i ), y s i ; g(x t j ), y t j ) = αc(g(x s i ), g(x t j )) + βL(y s i , y t j ) (4)

where c(•, •) is the squared 2 distance, L(•, •) is a cross-entropy loss that enforces regularity between the source and target domain labels, and α and β are two scalar values. Since no labels y t j are available in the target domain they are replaced with pseudo-labels f (g(x t j )) obtained from the classifier f : Z → Y. We seek for a transportation coupling γ ∈ R ns×nt in the space Γ(µs, µt) of joint probability distributions with marginals γ1n t = µs and γ T 1n s = µt, where 1 d is a d-dimensional vector of ones, and a pair of mapping functions g and f that minimize min γ∈Γ(µs,µt),g,f i,j γi,jd(g(x s i ), y s i ; g(x t j ), f (g(x t j ))).

(

) 5
We follow a two-step procedure to solve this optimization problem.

In the first step, we compute the optimal coupling matrix γ with fixed model parameters f and g,

min γ∈Γ(µs,µt) i,j γij(α||g(x s i ) -g(x t j )|| 2 + βL(y s i , f (g(x t j )))). (6)
In the second step, with fixed γ, we update the models g and f as

min g,f Ls + i,j γij(α||g(x s i ) -g(x t j )|| 2 + βL(y s i , f (g(x t j )))) (7)
where Ls correspond to the classification cost on the source domain to avoid losing performance on synthetic data.

Sampling strategy

For each data batch we sample all active and inactive frames from the source and target domains as indicated by the strong labels and the pseudo-labels. For both domains we only keep active frames where no sound event overlap occurs, so that the optimal transport takes place between the empirical distributions of the sound classes of both domains. The number of sampled active frames per class can vary considerably from batch to batch for synthetic and real data, which can lead to the absence of certain classes in one type of data for some batches. To account for this imbalance problem we only keep active frames from common classes to both domains, and then balance all classes by resampling them randomly, taking as many elements as there are in the class with fewer elements. Similarly, the number of inactive frames in the source and target domains varies from batch to batch, so we sample randomly each set by taking as many inactive frames as there are in the set with fewer elements.

Pseudo-label refinement

To improve the reliability of the pseudo-labels assigned to real data, we leverage the provided annotations of the weakly labeled set to refine pseudo-labels on this subset. The refinement process consists of fusing the frame-level outputs of the SED branch f on soundscapes from D W with their clip-level annotations by an element-wise multiplication. The target domain pseudo-labels are thus updated for weakly labeled data as ŷt j = f (g(x w j )) y w j , j = 1, . . . , nw. This operation constrains the estimated labels to contain at most the same classes present in the weakly labeled soundscapes. Filtering out all extra classes helps reduce false positives and allows more reliable pseudo-labels to be obtained for the proposed sampling strategy and domain adaptation process.

Training objectives

We denote as ẑs and ẑt the sampled active frames and as zs and zt the sampled inactive frames from the source and target domain latent representations z s and z t , respectively. After an initial pretraining stage using (3), we construct the following objective function to account for the mismatch between the empirical distributions of active and inactive learned feature representations

Ls + Lactive + Linactive ( 8
)
where

Ls = 1 ns ns i=1 L(y s i , f (g(x s i ))) + 1 ns ns i=1 L(y fb i , fFB(g(x s i ))) (9)
corresponds to the first and third classification cost terms of the training classification cost in [START_REF] Plumbley | Proceedings of the Detection and Classification of Acoustic Scenes and Events 2018 Workshop[END_REF]. As only the student model undergoes adaptation, no consistency losses are included in the above objective to train the source domain classifier. The cost function La corresponds to the distribution alignment loss of active frames

Lactive = 1 |Cactive| N active i,j γ active ij (α||ẑ s i -ẑt i || 2 + βL(y s i , ŷt j )) ( 10
)
where |Cactive| is the cardinality of the subset of labels Cactive ∈ C representing the total number of active classes in the batch. The second term in [START_REF] Copiaco | A study of features and deep neural network architectures and hyperparameters for domestic audio classification[END_REF] enforces consistency between the target domain pseudo-labels and source domain labels. The cost function Linactive accounts for the alignment of the marginal distributions of the learned representations of inactive frames in both domains:

Linactive = N inactive i=1 γ inactive ij (α||z s i -zt i || 2 ). (11)
Figure 2 depicts the proposed frame-level domain adaptation strategy based on optimal transport for the SED task.

EXPERIMENTS AND RESULTS

Model

The selected model architecture is the same as the baseline system of DCASE 2020. The CNN part is composed of 7 layers with 16, 32, 64, 128, 28, 128, 128 filters, respectively. A kernel of size 3x3 was used with max-pooling [START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF][START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF], [START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF][START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF], [START_REF] Plumbley | Proceedings of the Detection and Classification of Acoustic Scenes and Events 2018 Workshop[END_REF][START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF], [START_REF] Plumbley | Proceedings of the Detection and Classification of Acoustic Scenes and Events 2018 Workshop[END_REF][START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF], [START_REF] Plumbley | Proceedings of the Detection and Classification of Acoustic Scenes and Events 2018 Workshop[END_REF][START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF], [START_REF] Plumbley | Proceedings of the Detection and Classification of Acoustic Scenes and Events 2018 Workshop[END_REF][START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF] and [START_REF] Plumbley | Proceedings of the Detection and Classification of Acoustic Scenes and Events 2018 Workshop[END_REF][START_REF]Proceedings of the Detection and Classification of Acoustic Scenes and Events 2019 Workshop (DCASE2019)[END_REF], respectively. A gated linear unit activation is applied to the convolution operations. The RNN part is composed of 2 layers of 128 bidirectional gated recurrent units. The output of the CRNN is followed by a dense layer with sigmoid activation to produce frame-level (strong) class-wise posteriors. Clip-level (weak) scores are obtained by multiplying the aforementioned linear layer with a dense layer with softmax activation followed by mean temporal aggregation. The FB branch consists of a dense layer with sigmoid activation, which acts upon the outputs of the RNN block. The SEDFB branch is composed of a bidirectional RNN with 128 gated recurrent units and a dense layer with sigmoid activation.

Dataset and training procedure

We conducted experiments on the Domestic Environment Sound Event Detection Dataset (DESED) dataset [START_REF] Turpault | Sound event detection in domestic environments with weakly labeled data and soundscape synthesis[END_REF][START_REF] Serizel | Sound event detection in synthetic domestic environments[END_REF], composed of a training set of 2,584 synthetic audio clips generated by Scaper [START_REF] Salamon | Scaper: A library for soundscape synthesis and augmentation[END_REF], 1,578 real soundscapes with clip-level annotations and 14,412 unlabeled real recordings. In the training stage, the model was trained for 200 epochs with the Adam optimizer, a dropout value of 0.5, and a gradually increasing learning rate with a max value of 10 -3 [START_REF] Delphin-Poulat | Mean teacher with data augmentation for dcase 2019 task 4[END_REF]. The consistency weight λ was set to 1. In the adaptation stage, the student model was adapted for 300 epochs. We used cost weights α = 0.2, β = 5.0, and the contribution of the source domain classifier cost Ls to the total adaptation cost was multiplied by 100. The learning rate was fixed to 10 -4 . Experiments with optimal transport were performed using the Python Optimal Transport package [START_REF] Flamary | Pot: Python optimal transport[END_REF].

Results

In Table 1 we compare results obtained by the proposed methods on the validation and public evaluation sets of the DESED dataset in terms of the event-based macro F1 score. The model labeled as Baseline correspond to the baseline system of DCASE 2020 Challenge Task 4. Although the baseline system of the 2021 edition comprises the same architecture as Baseline, it cannot be compared with our methods as it was trained on a different synthetic dataset with data augmentation. For each evaluation set we show performance with median filtering (+MF) or HMM smoothing (+HMM) post-processing.

Adding the FB branch is beneficial to the SED task as it improved results on the validation set compared to Baseline by 8.3%. Further enhancement was achieved by refining outputs with HMM smoothing, as performance increased by 10.6%. Moreover, its fusion with the SED branch into a combined SEDFB branch brought an additional gain of 3% with median filtering. A similar trend is observed for the public evaluation set. Model adaptation with the proposed strategy increased performance over Baseline by 7.6% as a standalone method, and by 10.8% and 12.8% when combined with the FB and SEDFB branches. These results prove the effectiveness of the system in reducing mismatch between synthetic and real data. Compared to the validation set, performance was about 2% larger on the public set, which might be due to the fact that the empirical distribution of the active and inactive frames of this set resembles more that of the provided real training data on which adaptation was carried out.

HMM smoothing as a post-processing method yielded greater improvement to the scores over median filtering for all proposed models except for the SEDFB-based methods, in which +MF and +HMM provided similar scores, implying that the SEDFB branch plays a similar role as HMM decoding in the modeling of timevarying spectra of sound events. DCASE 1 and DCASE 2 are model ensembles comprising three and two + FB + DA systems from different training runs, respectively. Ensembling is achieved by simply averaging the model outputs. These models correspond to the submissions made to the DCASE 2021 Challenge Task 4 and are labeled as Olvera INRIA task4 SED 1 and Olvera INRIA task4 SED 2, respectively. Both systems showed competitive performance in terms of the event-based macro F1-score on the evaluation and public evaluation sets among 65 systems.

CONCLUSION

In this paper we proposed two methods that enhance the detection of domestic sound events. Motivated by the categorization of the spectro-temporal characteristics of domestic sounds as foreground or background, we proposed the use of an auxiliary foregroundbackground classifier that is jointly trained with the sound event classifier to improve generalization. Furthermore, we proposed to incorporate an adaptation stage based on the joint distribution optimal transport of feature embeddings and labels to account for the acoustic mismatch between the available synthetic and real training data. We showed that the multi-task training scheme together with the adaptation stage substantially improved the performance of the baseline system.

Figure 1 :

 1 Figure 1: Proposed model with colored data flow for synthetic and real data. For simplicity, the diagram depicts only the student model and the associated classification costs. The dash-lined path represents the training scheme with the fusion of the sound event detection and foreground-background classification branches.

  for the teacher model). The input for the SEDFB branch is the outer product of the outputs from the SED and FB branches wi = f (g(xi)) ⊗ fFB(g(xi)), as this fusion creates a representation containing information from the joint interaction of the SED and FB classifiers. The following classificationconsistency cost pair is added to the training objective in (1):

Figure 2 :

 2 Figure 2: Proposed adaptation method to correct domain mismatch.

Table 1 :

 1 Performance on the validation and public evaluation sets.

	Method	F1 score	F1 score
		val	val	eval	eval
		+MF	+HMMs	+MF	+HMMs
	Baseline	34.8		38.1
	+ DA	42.41	43.89	44.8	47.12
	+ FB	43.12	45.42	46.06	49.38
	+ FB + DA	45.68	47.77	50.79	53.10
	+ SEDFB	46.15	46.20	48.40	49.79
	+ SEDFB + DA	47.61	47.75	52.12	53.30
	DCASE 1	45.13	48.07	50.58	53.35
	DCASE 2	45.15	47.08	50.28	52.23