Hugo Fernandez-Mena
email: hugo.fernandez-mena@supagro.fr

Nicolas Guilpart

Philippe Lagacherie

Renan Le Roux

Nina Graveline

Jean-Marc Touzard

Hervé Hannin

Christian Gary

Grapevine yield big-data for soil and climate zoning. A case study in Languedoc-Roussillon, France

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

Introduction

In viticulture, zoning is based on the idea of 'terroir', which is the relationship between climate, soil, vine compartments, and farming practices to ensure wine quality and typicity [START_REF] Van Leeuwen | E3S Web of Conferences[END_REF]. Terroir was often based on traditional knowledge to delimitate zones, however, as some authors suggest, terroir studies should be more unbiased by using precision agriculture techniques to measure environmental data [START_REF] Bonfante | [END_REF]3]. For so, authors started using climate indicators for zoning, like in the MCC system (Multicriteria Climatic Classification) [4]. Recent studies combined both climate and soil indicators for viticultural zoning [5][6][7]. Although some studies have integrating grapevine yield data [8], no methods exist for directly classifying soil and climate indicators related to grapevine yield.

Compared to other crops, grapevine yield has been historically overlooked, assuming a trade-off between yield and wine quality [9]. Most European labels set limits on grapevine yields within the framework of geographical indications, but in many vineyards, producers cannot reach the maximum authorized yield. Historical grapevine yields in France have stagnated since the 1980s [10], and environmental and management drivers may be causing a "vineyard decline" [START_REF] Riou | BIO Web of Conferences[END_REF]. Climate change is also expected to have a particularly negative impact on grape yield in warm, dry winegrowing regions such as the Mediterranean [START_REF] Ollat | [END_REF]. Little is known about grapevine yields at large scales, with only recent studies analyzing water-limited grapevine yield gaps in the Barossa and Eden valleys [13].

In Languedoc-Roussillon, the Pays d'Oc Protected Geographical Indication (PGI) is particularly concerned about the long-term stability of its production levels, as yield is a main driver of individual wine estate performance and its long-term sustainability. All grapevine producers under the Pays d'Oc PGI quality label are subject to the same maximum yield requirements established by the label and most years, numerous producers are far from the yield limit. The PGI label supports exploring avenues for stabilizing yields at satisfactory individual and collective levels. Knowledge about environmental factors involved in grapevine yield will help to create potential adaptation measures to reduce yield gaps.

The objective of this study was to identify spatial zones within the wine-growing region of 'Languedoc-Roussillon' (South of France, south-eastern part of the French Occitanie region) based on climate and soil indicators linked to grapevine yield. To achieve this, we collected data from grapevine producers under the Pays d'Oc PGI quality label for a period of 9 years. The data was aggregated at the municipality level and we calculated the soil and climate indicators that influence grapevine yield at this level. We used scientific literature to determine the indicators that had a significant impact on grapevine yield at the municipality level and clustered the zones presenting similar indicators. This facilitated the identification of environmental resources. Our hypothesis was: (i) different combinations of climate and soil can result in different yield levels, (ii) the same yield level can be achieved with different combinations of climate and soils, and (iii) some grape varieties are preferentially cultivated in specific combinations of climate and soils with higher associated yields.

Selection of indicators by data mining

Grapevine yield data were obtained from harvest customs declaration data provided by producers under the Pays d'Oc PGI in the former Languedoc-Roussillon region. The dataset contains a total of 96,667 yield data for a period of 9 years (from 2010 to 2018), 58 grapevine varieties and 606 municipalities. Yield data was aggregated on a yearly basis at municipality level for all grapevine varieties and vineyards, resulting in 4455 annual municipality yield data. The PGI label sets a maximum red and white wine production limit at 90 hl•ha -1 •year -1 .

In our database, the vineyard cultivated area and wine volume as declared by the Pays d'Oc label were aggregated on the municipalities presenting a mean of 65.3 hl•ha -1 •year -1 , a median of 67.03 hl•ha -1 •year -1 . To fill the yield gap to reach label's maximum yield requirements for red and white wines (i.e. 90 hl•ha -1 • year -1 ) in all municipalities, a total volume of 684 318 hl•year -1 could be expected.

The estimation of average grapevine yield at the municipality level between 2010 and 2018 revealed localised yield gaps in numerous municipalities (Fig. 1). Temporally, no declining trend was observed within this time frame, although some years had lower yields, in particular 2010 and 2017, which were linked to severe drought conditions. Climate and soil data were aggregated at the municipality level. Average grapevine yield (hl•ha -1 • year -1 ) was calculated as the area-weighted average of yields over all grapevine varieties in each municipality. SAWC map raster was intersected with the municipalities of the region studied and an area weighted average of SAWC was calculated for each municipality [14]. We calculated the municipality soil pH as the average pH of several soil layers at depths of 0-5, 5-15, 15-30 and 30-60 cm [15]. The SAFRAN-Météo France weather data in 8x8km grid were aggregated at municipality level using the nearest neighbor method [16].

After identifying and calculating an initial set of climate and soil indicators relevant to grapevine yield, we used a backward stepwise model selection process using linear mixed-effect models to discriminate and select the statistically significant indicators [START_REF] Zuur | Mixed effects models and extensions in ecology with R[END_REF]18] capable of estimating grapevine yield at the municipality level. The indicators tested and selected are presented in Table 1.

We selected a mixed model that maximised AIC and BIC performance, for which 6 of the 10 calculated indicators proved to have a significant effect on the annual grapevine yield of the municipalities (n = 4455). This method obtained a low marginal R 2 (0.112), thus showing low potential for annual yield prediction. Yet, the same predictors proved to be more relevant for the prediction of average grapevine yield for the whole period (n = 606), with a marginal R 2 of 0.546 and a conditional R 2 of 0.627. The variables that were found to have a significant effect on grapevine yield at the municipality level were, in order of increasing significance: soil available water capacity, climatic dryness index, Huglin Index, days of frost, soil pH and the very hot days. Despite their theoretical impact on grape yield, four indicators were excluded from our model, presented in Table 1. Based on these indicators, we clustered the municipalities with similar soil and climate, helping us to create groups of municipalities, hereon, referred as zones. For the clustering, we used a combination of principal components analysis and ascendant hierarchical classification [19].

Zoning results

The principal components analysis and ascendant hierarchical classification helped to define seven clusters of municipalities using the selected soil and climate indicators. Each of those clusters represents an agroecological zone with similar soil and climate characteristics that favours or constrains grapevine yield. The zones are spatially displayed in Fig. 2 and their soil and climate characteristics are explained as follows. Zone 1 is the 'Humid zone of the hinterland' and has the coolest temperatures due to its distance from the Mediterranean coast. As a consequence of having the lowest Climate Dryness Index (around -150 mm) and number of Very Hot Days (from 0 to 2), this region benefits from high grapevine yield. Its main constraint is its Huglin Index, which is the lowest, with 300-400 degree-days less than other zones. The Soil Available Water Capacity is relatively high (from 70 to 100 mm) and Days of Frost are average (from 10 to 20).

Zone 2 is the 'Zone with acid and shallow soils in the mountains', which is the only one with an acid soil pH (ranging from 5 to 7.5), which constrains grapevine yield. This zone also has the lowest soil available water capacity (from 50 to 80 mm) and a low Huglin Index. The rest of the variables are average. The municipalities of this zone are located at the highest elevations with municipalities in the southern (Pyrenees mountains) and northern (Caroux Mountains) areas of the region.

Zone 3 is the 'Zone of piedmont with constraining SAWC'. It has low temperature-related variables, similar to those in Zone 2, but municipalities in this zone have alkaline soil pH (from 7 to 8.3). Water-related indicators are also not very favourable, although is significantly higher than in Zone 2. The municipalities of this zone are located at mid-elevation and in the piedmont areas of the region.

Zone 4 is the 'Cold and dry zone surrounding Pic St Loup'. This zone is constrained by numerous Days of Frost, but high temperatures in summer. This zone is also constrained by low water availability from rainfall and low Soil Available Water Capacity. The municipalities of this zone are located in high areas surrounding the peak Saint-Loup (north of Montpellier).

Zone 5 is the 'Zone of average inland soils'. It comprises relatively average soils, although Soil Available Water Capacity is very variable. The region is constrained by a high Climatic Dryness Index and the highest Huglin Index. The municipalities of this zone are mainly located on the inland plains in the central and eastern parts of the region.

Zone 6 is the 'Zone with deep soils in mild coasts'. It comprises the best soils (highest Soil Available Water Capacity), compensating for having the highest water deficit (highest Climatic Dryness Index) in the region. Extreme temperatures are rare in this zone due to the proximity of the sea.

Zone 7 is the 'Highest number of very hot days but deep soils'. It is subject to the most extreme temperatures with the highest level of Very Hot Days and many Days of Frost. In contrast, water availability is favourable due to deep soils (high Soil Available Water Capacity) and lower Climatic Dryness Index. The municipalities of this zone are located on several inland plains in the eastern part of the region. Depending on their average yield distribution, the clustered zones can be divided into two main groups (Fig. 3):

1. The group with the lowest yields, ranging from 50 to 60 hl•ha -1 •year -1 . This group corresponds to municipalities in Zones 2, 3 and 4. Within this group, Zone 3 has a significantly higher yield.

2. The group with the highest yields, ranging from 65 to 80 hl•ha -1 •year -1 , which corresponds to the municipalities of Zones 5, 6 and 7.

Municipalities in Zone 1 show an intermediate yield gap between the two above-described groups. We observed a high variation in yield levels depending on the zones as shown by the coefficient of variation in Fig. 3. Although over time there was not a significant tendency towards lower yields in the zones, the zones with low yields (i.e., Zones 2, 3 and 4) drastically reduced their yields in occasional years. Zones 5 and 6 account for the highest cultivated areas (i.e., 20000 to 25000 ha) and Zones 4 and 2 for the lowest (i.e., 1000 to 2500 ha).

Conclusion and perspectives

The current study proposes a methodology for selecting theoretical climate and soil factors that could significantly impact grapevine yield at the municipality level. By conducting research at this scale, it is possible to acquire further insights into winegrowing landscape characteristics that could facilitate future studies on vineyard management practices. Our analysis revealed six pertinent factors that accounted for grapevine yield at R 2 = 0.546, which only partially explained grapevine yield. Future research should consider a longer yield and the time-span of the climate database to enhance the precision of indicator selection.

We opted to employ clustering to aid in the analysis of the types of municipality with comparable soil and climate characteristics. The decision to apply this zoning approach was also driven by the fact that it offers a foundation for creating R&D recommendations. Based on statistical clustering carried out with the guidance of regional wine label experts, we divided the Languedoc-Roussillon region into seven distinctive zones that had two contrasting yield gap levels linked to distinct indicator combinations related to the limitation of grapevine yield. For each zone, we ascertained the extent to which pedoclimatic factors could account for the variability. Understanding the limiting factors associated with each zone could assist local experts in implementing adaptation measures to prevent or limit grapevine yield loss.

In this study, we demonstrated that environmental factors at this scale could account for a small portion of the annual variability of yield but a significant portion (>50%) of the average yield over time. Further research is necessary to examine the interactions between plant material and farming practices within each zone, as they may also play a crucial role in grapevine yield gaps at the regional scale.

Figure 1 .

 1 Figure 1. Municipality average grapevine yield (weighted by their area for all grapevine varieties) in Languedoc-Roussillon of Pays d'Oc PGI labelled wines between 2010 and 2018 (n = 606 municipalities). Top left: histogram of the displayed data for all municipalities and 9 years between 2010 and 2018 (n = 4455) averaged from individual yield declarations (n = 96677).

Figure 2 .

 2 Figure 2. Soil and climate zones related to grapevine yield at the municipality level in Languedoc-Roussillon.

Figure 3 .

 3 Figure 3. Distributions of average municipality grapevine yields (n= 606) in hl•ha-1•year-1 in each of the seven clustered zones in Languedoc-Roussillon between 2010 and 2018. The boxplots represent the distribution in quartiles with median lines. Circles represent the mean and filled dots are outliers. Letters correspond to Tukey's range test for comparison of means. The dashed red line corresponds to the 90 hl•ha -1 •year -1 maximum label yield used for yield gap calculation. The percentage in brown corresponds to the coefficient of variation over time for each zone.

Table 1 .

 1 Soil and Climate indicators as Yield predictors.

	Variable

name Units Average p-value selection or exclusion Grapevine yield

	Municipality average grapevine yield	hl•ha -1 •year -1 67.03
	Soil
	Soil Available Water	mm	88.79	***
	Capacity
	Soil pH	-	7.91	**
	Climate Climatic Dryness Index	mm	-221.6	***
	Huglin Index	°C	2270	***
	Days of Frost	days	16.76	***
	Frequency of Late Frost	days	0.01	excluded
	Severity of Late Frost	°C	0.0002	excluded
	Hot Days	days	31.83	excluded
	Very Hot Days	days	1.8	**
	Severity of Heat Stress	°C	2.16	excluded

© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (https://creativecommons.org/licenses/by/4.0/).

BIO Web of Conferences 68, 01043 (2023) https://doi.org/10.1051/bioconf/20236801043


Matej Mayet
email: matej.mayet@dalembert.upmc.fr

Jean-Loïc Le Carrou
email: jean-loic.lecarrou@sorbonne-universite.fr

David Gueorguiev
email: david.gueorguiev@sorbonne-universite.fr

Perception of Friction-Related Cues Induced by Temperature Variation on a Surface Display

Keywords: thermal haptics, friction modulation, surface haptics

Frictional cues enable us to perceive material properties and topography, which has prompted a dynamic research on methods for friction modulation. Recently, a novel method based on local heating of a screen was proposed for modulating friction and create the sensation of shape when exploring the surface. We built a setup able to reproduce this method to investigate how three parameters, the width of the heater, its temperature, and the duration of the pre-heating before the interaction, influence perception of purely tactile cues. The results show that raising the temperature of the heater increases the perception of tactile cues but that the width of the heater or the pre-heating duration had no effect on it. Surprisingly, the increase of the coefficient of friction at the heated location was only impacted by the width of the heater and the pre-heating duration. Our study confirmed that non-thermal tactile cues can be induced by local heating of a tactile display but we did not observe a direct relationship between the variation of the coefficient of kinetic friction and perception.

I. INTRODUCTION

The importance of a haptic feedback while interacting with an object is central to humans [START_REF] Johansson | Coding and use of tactile signals from the fingertips in object manipulation tasks[END_REF]. Whether it is a thermal or a mechanical feedback, it increases the immersion and enables the user to adapt and react according to tactile afferent information [START_REF] Macefield | Control of grip force during restraint of an object held between finger and thumb: Responses of muscle and joint afferents from the digits[END_REF], [START_REF] Dimitriou | Discharges in Human Muscle Receptor Afferents during Block Grasping[END_REF].

During the last two decades, research on how to integrate a feedback stimulating the sense of touch in a device has largely developed [START_REF]Immersive Multimodal Interactive Presence. Springer Series on Touch and Haptic Systems[END_REF], and haptics are now a growing subject of interest in several fields [START_REF] Hirche | Human-Oriented Control for Haptic Teleoperation[END_REF]- [START_REF]Musical Haptics. Springer Series on Touch and Haptic Systems[END_REF]. However, we can observe quite universally a lack of haptics in interactive devices such as tablets or smartphones. These devices can provide complex visual and auditory cues, but its haptic feedback is still often limited to a buzzing sensation that transmits to the user an information of a poor nature [START_REF] Culbertson | Haptics: The Present and Future of Artificial Touch Sensation[END_REF].

One of the challenges with these devices is to integrate a tactile feedback coming from the part the user directly interacts with (i.e. the screen of the smartphone), whose actuation represents a serious challenge to the development of novel Surface Haptic Devices (SHDs). Currently, two major methods exist for rendering frictional cues on displays: ultrasonic lubrication and electroadhesion [START_REF] Basdogan | A Review of Surface Haptics:Enabling Tactile Effects on Touch Surfaces[END_REF]. Ultrasonic lubrication consists in vibrating a glass plate interface at an ultrasonic frequency to generate a squeeze film effect between the interface and the finger of the user, which results in a decrease of friction [START_REF] Wiertlewski | Partial squeeze film levitation modulates fingertip friction[END_REF], [START_REF] Gueorguiev | The Perception of Ultrasonic Square Reductions of Friction With Variable Sharpness and Duration[END_REF]. One of the major challenges with this method is to sustain uniformity in the amplitude of the vibrations throughout the plate, especially when the size of the plate gets bigger. On the other hand, electroadhesion (or electrovibration) aims at increasing the friction between the surface and the finger. The contact between the finger, an electrical conductor, and the charged surface results in an augmentation of the electrostatic attraction force [START_REF] Bau | TeslaTouch: Electrovibration for touch surfaces[END_REF], [START_REF] Guo | Electroadhesion Technologies for Robotics: A Comprehensive Review[END_REF].

In addition to these two well-known methods, a novel method able to perform a localized change of friction on a surface was proposed by Choi et al. [START_REF] Choi | Effect of Surface Temperature on Finger Friction and Perception in Electroadhesion[END_REF], [START_REF] Choi | Surface haptic rendering of virtual shapes through change in surface temperature[END_REF], based on studies that demonstrate the close relation between the viscoelastic properties of skin-like materials and their temperature [START_REF] Tiwari | Rubber friction: The contribution from the area of real contact[END_REF], [START_REF] Ludema | The friction and visco-elastic properties of polymeric solids[END_REF]. This method has the advantage of not being as power consuming and complex to implement as the methods mentioned above. The results of Choi et al. show that when exploring a glass plate, the temperature of the surface has an impact on the mechanical properties of the fingertip's outer layer. Specifically, increasing the temperature of the plate decreases the mechanical rigidity of the fingertip when in contact, causing an increase of the real contact area between the skin and the interface, inducing greater frictional forces. At controlled pressure force and sliding speed, [START_REF] Choi | Surface haptic rendering of virtual shapes through change in surface temperature[END_REF] observed an increase in friction of about 50% when the surface temperature increases from 23°C to 42°C. They suggest that the physical mechanism responsible for this change of friction is due to temperature dependency of both the viscoelastic modulus and moisture level of the fingertip. Based on these observations, they designed three-dimensional (3D) shapes generated by changes in friction on a two-dimensional (2D) surface. They were able to create a Surface Haptic Device (SHD) consisting in a flexible heater diffusing heat at the middle of a glass plate. The device creates a temperature gradient on the surface which causes the friction forces to vary across the plate. Using this device, they suggested that friction force could be modulated up to 0.4 N. Such an increase in friction force corresponds to a 6 mm high bump according to the relationship between the lateral force and a Gaussian shaped bump [START_REF] Robles-De-La-Torre | Force can overcome object geometry in the perception of shape through active touch[END_REF]. When sliding their finger across the glass plate, the participants were able to correctly locate the heater from 76% to 96% of the cases. While their finger crossed the heated zone, participants felt a "bump" or a "sticky zone", sensations likely induced by the increase of friction within the heated zone [START_REF] Johansson | Coding and use of tactile signals from the fingertips in object manipulation tasks[END_REF]. The study also explored how strongly the exploration speed and the normal force applied by the finger on the surface impacted the coefficient of kinetic friction [START_REF] Choi | Surface haptic rendering of virtual shapes through change in surface temperature[END_REF].

In this study, we aim at expanding the knowledge about the potential to induce frictional cues with localized heat bands. To that end, we propose a parametric study that explores how parameters such as the width of the heater, its temperature, and the pre-heating time impact the perception of tactile and thermal cues on a plane surface. We also investigate how the variation of these parameters influence the coefficient of kinematic friction between the plate and the fingertip during sliding.

II. MATERIALS AND METHODS

A. Experimental setup

For this study we built a device able to change the temperature profile of a glass plate and to measure the forces generated by the interaction of a fingertip on the surface. An illustration of our experimental setup is shown in Fig. 1. The normal and tangential forces between the fingertips and the glass surface were measured with a 6 axis force / torque sensor (FTN-Mini-40 SI-20-1, Schunk) with a 0.01 N resolution on -→ X and -→ Y , and 0.02 N on -→ Z . Signal was digitalized at 1 kHz by a 16-bit acquisition card (PCIe-6323, National Instruments) and filtered by a low-pass Butterworth filter with a 45 Hz cutoff frequency. The force sensor was held to the table with a fixed 3D printed support (PLA) such as its -→ Z is collinear to table's normal axis. The support was tightly fixed to the table using 2 screws and an aluminium bar. On the top of the sensor, a 3D printed support (PLA) was maintaining the glass plate unmoving. The glass plate interface was made out of clear glass whose dimensions are 9.95 mm × 8.30 mm × 1.00 mm (± 0.01mm). This plate was graduated so that the heater was centered at the same point every time, independently from its size. The polyimide heating plate (10 mm × 93 mm polyimide heater plate, Icstation) was then fixed under the glass plate to generate a temperature gradient at its surface (see Fig. 2). Three models of heaters were available : the regular heater was left as it is, the thin model was obtained by cutting the regular one in half, and the large heater by putting two regulars side by side. A DC generator (VSP 1220,Voltcraft) was used to power the heaters during the experiment. Finally, a Neonode sensor (zForce Air 90°, Neonode) was fixed on the side of the Glass Support in order to get the position of the user's finger moving on the plate. The sensor detects and traces the finger with a resolution of 0.1 mm along both -→ X and -→ Y axis by detecting diffusely reflected infrared light it emitted previously (see Fig. 1-(B)).

B. Experimental procedure

The goal of this experiment was to perform a parametric study highlighting the impact of three specific parameters on both the modulation of friction and participants' feeling, during a 5 seconds long exploration of the surface with the fingertip. These parameters are: the width of the heater, the temperature of the heater, and the pre-heating duration. We chose to test three levels for each parameter, allowing 27 possible combinations. The numerical values taken by all three parameters are shown in Table I. We chose heater temperature as a parameter rather than the surface's temperature since the heater's temperature could be more consistently controlled within the trials than the latter. A total of 9 participants took part in the experiment (7 males and 2 females, all right-handed and with no reported injury or impairment to the hand). Each participant was independently brought into an air conditioned room set at 19°C; their hands and the glass plate were cleaned with isopropyl alcohol, and they were asked to take a 10 minute pause before the experiment in order to let their body acclimatize to the controlled environment.

At each trial, the participant explored the glass plate with the index fingertip for 5 seconds (see Fig. 1). 27 timestamped trials were performed, one for each combination. In addition, the participant had to perform a "control exploration" where a heater was placed but not activated without the participant being aware of it. In total, the experiment consisted of 28 trials lasting 5 seconds, with mandatory pauses between each trial for the glass plate to return to room temperature.

For each trial, the participant was told to cross the glass plate along -→ Y about 4-5 times, and to apply a normal force not exceeding 0.8 N. Before the experiment started, the participant had to perform a monitoring session to acquaint with the setup and the rules of the experiment. These rules were set to prevent extreme behaviors, but they allowed for some flexibility to the way the participant could explore the plate in terms of speed, trajectory and normal force applied. Every trial was conducted the same way: participants first start to explore the surface with their index fingertip for 5 seconds, they have then 20 seconds to fill a multiple-choice questionnaire based on what they felt while exploring. Once they have filled it they are asked to wait until the next trial is ready.

This experiment uses a device generating haptic feedback through a variation of temperature on its surface. To understand what kind of tactile stimulus is mainly felt with such a device, we set a predefined number of categories in the questionnaire. The participant had to choose amongst five categories of stimuli to describe best what they felt: an edge, a bump, a sticky zone or heat. They could choose as many categories as needed, or none in case they did not feel anything. These categories were the same for every participant and were mainly based on the results reported in [START_REF] Choi | Surface haptic rendering of virtual shapes through change in surface temperature[END_REF].

C. Coefficient of Friction (COF)

We computed the coefficient of kinetic friction µ k , defined as

µ k = F y F z
where F y is the norm of the tangential force along -→ Y and F z is the norm of the normal force along -→ Z (see Fig. 1). The coefficient of kinetic friction was used to assess the stimuli's impact on the friction that the fingertip experiences during the exploration. In this paper, we will refer to µ k as the coefficient of friction (COF). Figure 2 shows the evolution of the COF according to the position of the finger on the plate for the trial n°28 of the participant n°7. The heatmap of the glass plate above the graph is specific to this trial but is very similar for the other participants. The heat distribution was measured with an infrared camera (C5, FLIR) and fitted with an 8 th order Gaussian function.

In order to quantify the impact of temperature modulation on friction, we measured the average COF in three intervals: before, during, and after the finger crossed the heater (hence the use of a position sensor).

For that sake, we defined 3 zones on the glass plate, as shown in Fig. 2. The shaded red zone corresponds to the area occupied by the heater on the plate. We defined two boundaries on the plate located where the temperature gradient was at 60% of its maximum. These boundaries defined three zones: the spatial interval between the two boundaries, the shaded green zone at the left of the heater (LZ) and the one at the right of the heater (RZ) both corresponding to areas explored before or after the heater was crossed, depending on the sliding direction. The spatial width of the right and left zones was defined identical as the heater zone to enable consistent comparisons while the distance between the zones depended on the temperature gradient which was trial specific.

We then measured the average COF in each of the three zones and calculated its variation between zones. Despite the symmetry of the temperature gradient, we noticed overall strong differences in the COF values between before and after the participants have crossed the heater. Consequently we decided to separate them for our analyses, and since crossing the heater seems to affect the COF up to the end of the sliding, we chose to study the change of the COF only between its value in the heater's area and the zone that was explored just before.

As slidings were executed in both directions along -→ Y , the zone to which we would compare the heater's COF was relative to the direction of motion: when the participant slid towards Y = 0 mm we compared the average COF of the Heater zone noted µ heater to the average COF of RZ noted µ bef ore ; when the participant slid towards Y = 120 mm we compared the average COF of the Heater zone to the average COF of LZ noted µ bef ore .

COF var (%) = ⟨µ heater ⟩ × 100 ⟨µ bef ore ⟩ (1)
As highlighted in Fig. 2, the COF amplitude is significantly different when sliding in one or in the other direction. And even though we tried to control as many parameters as possible in this experiment, the unique physiology of each participant could not be controlled and has an impact on the COF. Thereby, throughout the experiment, the COF changes were calculated as a percentage of variation (see Eq. 1).

We hypothesized that when the participants were exploring the glass plate, they either relied on the full length of the exploration to build their perception, or they identified the most salient sensation and based their answers according to this particular feeling. Therefore, we analysed our experimental data for both cases:

(1) For each tactile stimulation within a trial, we measured the corresponding COF variation. All the variations were averaged to obtain the COF variation corresponding to the trial. The values for each type of trial were then averaged amongst all participants, which provided a mean variation value for each specific trial (Fig. 4-(A)). This variation is referred to as the "Mean coefficient of friction variation". (2) For each tactile stimulation within a trial, we measured the corresponding COF variation but selected only the biggest COF variation amongst the full length of the exploration. This maximal COF variation for each trial was then averaged amongst all participants, which provided a maximal variation value for each specific trial (Fig. 4-(B)). This variation is referred to as the "Maximal coefficient of friction variation".

III. RESULTS

A. Psychophysical results

First, we estimated how often the possible types of sensation that participants could report occurred during the psychophysical tasks. Results showed that participants felt predominantly non-thermal sensations (Fig. 3). A one-way ANOVA analysis with a Geisser-greenhouse correction confirmed a difference between the reported cues (F (2.469, 19.75) = 5.400, p = 0.01) and a post-hoc Tukey test showed a significant difference between reporting the feeling of a sticky area and reporting a hotter zone. Moreover, none of the participants reported a sensation in the first trial in which no heating was performed.

To investigate the impact of the experimental conditions on participant's perception, we performed a Generalized Linear Model analysis, in which a logistic binary model was selected. The independent variables were the temperature of the heater, the width of the heater, and the pre-heating duration. The dependent variable was defined as the perception of at least one of the proposed tactile sensations with the exception of heat. The results showed only a significant effect of the temperature of the heater (χ 2 = 4.082, df = 2, p < 0.001). The statistical analysis showed no significant interaction between the independent variables.

B. Analysis of the Coefficient of kinetic friction

First, we analysed the impact of each parameter related to the heater on both the mean and the maximal COF variation. A GLM statistical analysis showed a significant impact on the mean variation of the COF by the width of the heater (F (2, 14) = 10.43, p = 0.002) and the duration of the preheating (F (2, 14) = 6.61, p = 0.1) but not by the temperature of the heater (F (2, 14) = 0.45, p = 0.64). A post-hoc analysis performed with Bonferroni-corrected pairwise t-tests showed that all differences between the different heater widths are significant (p < 0.05) for the mean variation of the COF. Only the difference between 30 s and 240 s was significant for the duration of the pre-heating (n = 72, t = 3.654, df = 71, p = 0.0015).

As for the impact of the independent variables on the maximum increase in the COF that occurred in each trial, the GLM statistical analysis showed an impact of the two same independent variables as for the mean variation of the COF. The width of the heater (F (2, 14) = 16.80, p < 0.001) and the duration of the pre-heating (F (2, 14) = 6.61, p = 0.1) had a significant impact on the maximum increase of the COF but A post-hoc analysis performed with Bonferroni-corrected pairwise t-tests showed that all differences between the different heater widths are significant (p < 0.0001) for the maximum variation of the COF. Only the difference between 30 s and 240 s was significant for the duration of the pre-heating (n = 72, t = 3.219, df = 71, p = 0.006).

Once we found which parameters impacted either the perception or the COF variation, we further investigated the impact the COF variation amplitude had on perception. To that end, we conducted a correlation analysis on the data represented in Fig. 5, which depict the relationship between the mean COF variation and the percentage of participant who perceived a non-thermal sensation. It appears that there is no correlation between participants' perception and the mean COF variation (r = -0.03, p = 0.88). The same correlation analysis was performed with the maximal COF variation and there no correlation was found between participants' perception and the maximal COF variation either (r = -0.05, p = 0.81).

IV. DISCUSSION

First of all, the psychophysical results show that this method generates mainly non-thermal haptic cues. Thereby, our observations confirm previous research that showed that it is possible to create a tactile effect without triggering a large thermal response. Thus, this method fulfills its purpose but we noticed that the intensity of the haptic feedback was relatively subtle and participants did not feel the tactile cues as obvious. Our results also showed that varying the temperature of the heater had a significant impact on participants' perception, but that changing the values of both the width of the heater and the pre-heating duration does not impact the perception of non-thermal sensations. In previous studies, shape perception was triggered by a large change in the coefficient of kinetic friction [START_REF] Choi | Surface haptic rendering of virtual shapes through change in surface temperature[END_REF]. We calculated the variation of the coefficient of friction for each sliding through the heater and performed a statistical analysis on two measures of COF variation: averaged across all the slidings occurring within the trial, and the maximal change of friction that occurs when the finger goes across the heater during the trial. The analyses show that varying the width of the heater or the pre-heating duration has a significant impact on COF variations. These results are somewhat astonishing considering that only the temperature of the heater had a significant impact on the perception of tactile cues and that [START_REF] Choi | Surface haptic rendering of virtual shapes through change in surface temperature[END_REF] suggested that the haptic stimulus perceived by the participants is likely generated by the variation of the COF during the sliding.

Following this assumption, we hypothesized that the larger the coefficient of friction the bigger the proportion of participants that perceived a stimulus would be. However, the correlation study we conducted between the COF and the percentage of participants who perceived a non-thermal cue (Fig. 5) shows no correlation between participants' answers and the variation of the COF. This means that the coefficient of friction as calculated in our study does not relate to the perception of the tactile cues.

Still, these results do not rule out the role of frictional cues in the perception. It is possible that participants used transient frictional cues to which touch is especially sensitive [START_REF] Gueorguiev | The tactile perception of transient changes in friction[END_REF]. These variations might be captured by more precise measurements. Moreover, participants were left with some freedom to perform exploratory movements with their preferred speed and normal force. Individual differences might also have impacted the time course of the frictional variation and made them less salient in the analysis.

Regarding both mean (Fig. 4-(A)) and maximal (Fig. 4-(B)) COF variations, we observed the expected increase in the coefficient of kinetic friction. Interestingly, both graphs show strong similarities. In Choi et al. study, a COF augmentation of about 50% was measured between an exploration of a surface at 23°C and a surface at 42°C, our results show the maximal COF variation for a 15 mm wide heater is relatively close to this value.

V. CONCLUSION

This paper investigates the viability of friction variation by temperature modulation to generate a haptic stimulus when applied to a surface. This phenomenon is due to the particular properties of the stratum corneum, the outermost layer of human skin, which when heated decreases its mechanical rigidity, increasing the real contact area. We built a surface haptic device that uses this phenomenon, and were able to thoroughly investigate the impact of this technique on perception of nonthermal cues and finger-surface friction.

Lastly, we confronted our results to the ones obtained by [START_REF] Choi | Surface haptic rendering of virtual shapes through change in surface temperature[END_REF], and found similarities in the perception study and differences regarding the modulation of the COF. However, when increasing the width of the heater we observed a convergence towards the same results in terms of COF modulation. Yet, we did not observe a direct relationship between the variation of the coefficient of friction and perception, which is somewhat astonishing considering the initial assumptions and the psychophysical results from [START_REF] Choi | Surface haptic rendering of virtual shapes through change in surface temperature[END_REF]. Generally, the apparition and development of friction modulation by temperature variation opens new opportunities in this field of research, which might prove valuable for future haptic devices. More specifically, we imagine future devices applying this method to surfaces on which frictional and thermal dimensions are simultaneously rendered.

Fig. 1 .

 1 Fig. 1. (A) Experimental setup where the finger slides along -→ Y (blue arrows). (B) Upper view of the experimental setup, the position sensor sweeps and get the position of the finger on ( -→ X , -→ Y ) plane.

Fig. 2 .

 2 Fig. 2. COF computed during the trajectory of the finger along Y axis for a one-participant 5 s trial. Blue and red dots indicate the direction of the sliding. Red area shows the heater location. Green areas are the same width as the heater for measurement consistency. They start at 60% of the highest temperature on the left (LZ) and on the right (RZ) of the heater. The heat distribution on the plate along Y axis is shown by the colorbar above.

Fig. 3 .

 3 Fig. 3. Percentage of the trials in which a tactile or thermal sensation was perceived (Mean ± S.D). The slightly detached barplot on the right represents the percentage of trials in which at least one type of non-thermal stimulus was perceived.

Fig. 4 .

 4 Fig. 4. Mean COF variation (A) or Maximal COF variation (B) in percent for each trial. The shape and the fill color of each dot indicate the pre-heating duration and the width of the heater, respectively. Color zones represent the temperature at which the heater was set. Errors bars represent the mean and standard deviation (S.D.) of 9 repetitions for each trial. Mean COF variation (C) and Maximal COF variation (D) in percent for each condition: the pre-heating duration and the width of the heater. The barplots depict the Mean and S.D. and the data points represent individual values for a specific trial.

Fig. 5 .

 5 Fig. 5. Mean COF variation in percent for each trial, in function of the proportion of participants that felt a stimulus during the exploration. The shape, the border color and the fill color of each dot indicate the width, the temperature and the pre-heating duration of the heater, respectively. The brackets indicate the same proportion of participants that felt a non-thermal sensation. Error bars represent the Mean and S.D. for each type of trial.

VI. ACKNOWLEDGMENTS

We thank the UFR 919 of Sorbonne Université and the ANR 20-CE33-0013 (Maptics) for funding this research.


Asterios Katsifodimos

Ioana Manolescu

Alin Tilea

Spyros Zoupanos

Adaptive distributed XML views

come

We have designed and built ViP2P (standing for Views in Peer-to-Peer, a platform enabling peers to share XML documents by means of materialized views. Any ViP2P peer can publish XML documents and/or views described by conjunctive XML tree pattern queries. Once a view is published:

• the view definition is indexed in a distributed fashion over the network;

• the view is maintained, that is, documents published before or after the view will contribute data to the view extent. The view definition index is used by the publisher of a document to learn which views may stand to receive data from the document.

• views may be used to rewrite subsequent queries. The view definition index is used by the peer where a query is asked, to determine which views may be used to rewrite the query.

The architecture and algorithms for view indexing, maintenance and view-based query rewriting have been described in a separate paper [START_REF] Manolescu | Materialized views for P2P XML warehousing[END_REF]. Importantly, in that work, we considered the set of views on each peer to be given and immutable.

In this paper, we consider an important complementary problem: how to chose the materialized views to be established by each peer. Since in a datasharing network the data and query loads vary in time, the set of views must also change with time. Therefore, we discuss adaptation strategies which may change the set of views of a peer, to improve the performance of the peer's queries and that of queries to which the peer contributes.

This paper is organized as follows. Section 2 presents the language we use to defined views and queries, and the different classes of materialized views supported in ViP2P. Section 3 recalls the basic strategy of indexing and maintaining views, and re-using them to rewrite queries, in order to make this paper self-contained. Section 4 discusses view adaptation.

ViP2P materialized views 2.1 Patterns

We will rely on a tree pattern dialect P, defined as follows.

1. Pattern nodes can correspond to XML internal nodes (elements or attributes), or to leaves (words in text occurring inside XML elements, or in attribute values). For presentation purposes, we do not distinguish between elements and attributes. We extend the XPath descendant axis to consider that words are children of their closest element or attribute ancestors. Each internal pattern node carries a label from a tag alphabet A l = {a, b, c, . . .}. Each leaf node carries a label from a word alphabet A w = {a, b, c . . .}.

2.

Pattern edges correspond to parent-child or ancestor-descendant relationships between nodes.

3. Each pattern node may be annotated with some stored attributes, describing some information items that the pattern stores out of each XML node matching the pattern node. The cont annotation indicates that the full (serialized) image each matching XML tree node is stored. The id annotation indicates that a node identifier, which uniquely identifies the node (and the document it belongs to). Moreover, we assume structural IDs, i.e. such that one may decide, by comparing the identifiers of two nodes n 1 and n 2 , whether n 1 is an ancestor/parent of n 2 or not. Many variants of structural identifiers exist, e.g., [START_REF] Al-Khalifa | Structural Joins: A Primitive for Efficient XML Query Pattern Matching[END_REF][START_REF] Lu | From Region Encoding To Extended Dewey: On Efficient Processing of XML Twig Pattern Matching[END_REF][START_REF] Tatarinov | Storing and querying ordered XML using a relational database system[END_REF], some of which provide further information, e.g. allow identifying the least common ancestor of two nodes etc. For the purpose of this work, we only require that parent-child and ancestor-descendant relationships can be determined from the node IDs. Finally, the val labels stands for the node's text value, obtained by concatenating all its text descendants in document order.

4. Each node may be annotated with a predicate of the form [val = c] where c ∈ A w , restricting the XML nodes which match the pattern node, to those satisfying the predicate.

Notations and syntax simplification We say a pattern node has an id, respectively val, cont, or value predicate, if the node is decorated with such an index.

We introduce a simple text syntax for patterns. We denote nodes by their A l or A w label. The possible id, val and cont labels, and predicates over val, are shown as indices to the node. For instance, a id cont is a pattern storing the structural IDs and the content of all a elements. We use parenthesis to show the nesting of children inside parents, and commas to separate the children of the same pattern node among themselves. For instance, a(b(c id )) stores the IDs of elements found on some path matching //a//b//c. The pattern a [val=5] (b, c id ) stores the identifiers of all c elements having an a ancestor of value 5, and whose serialized XML subtree contains the word b.

Pattern semantics Let p be a pattern and d be an XML document. As customary, an embedding φ : p → d of p in d is a function associating d nodes to p nodes, preserving node labels and ancestor-descendant relationships [START_REF] Amer-Yahia | Tree pattern query minimization[END_REF]. The result of evaluating p on d, denoted p(d), is the list of tuples obtained by lining together in a tuple, all IDs and/or values and/or serialized content, for each embedding of p in d. Assuming a total order over the nodes of p (top-down, left-to-right traversal), the tuple order in p(d) is dictated by the lexicographic order over the d nodes which are targets of the embeddings. For a document set D, the semantics of p over D is defined as the concatenation (in the order of the document IDs) of all p(d), d ∈ D.

We use a.id (respectively, a.val, a.cont) to denote the corresponding attribute in p(D).

From patterns to views

Based on tree patterns, we are now ready to present ViP2P views. The main idea is that while a pattern may express fine-granularity structural conditions over an XML document, we allow two different granularities for materialized views: either document level, or node level. Document level views A document level view v dg includes exactly one tuple for any document d such that v dg = ∅. That tuple contains only the document URI. With respect to notation, we distinguish views at the document level by the fact that they do not have any id, val or cont attribute. Figure 1 presents 3 examples. View v 1 stores the URIs of all the documents that may have a node labeled a. View v 2 stores the URIs of all documents that have an a node which has a descendant b node, which has a descendant a c node. More generally, any tree pattern previously described, stripped of all its stored attributes, can become a document level view. Node-level views A node level view is defined by any pattern p ∈ P, and stores the result of evaluating p(d) over all documents d ∈ D (D is the set of documents published in the ViP2P platform).

Figure 2 shows a sample document, a node lavel view and the result of evaluating that view over that document.

Outline of ViP2P processing

To make this paper self-contained, we briefly recall from [START_REF] Manolescu | Materialized views for P2P XML warehousing[END_REF] how views are maintained and advertised in ViP2P (Section 3.1) and how queries are processed (Section 3.2. Concerning this last aspect, we explain how to process queries involving document-level views. Such views were not considered in [START_REF] Manolescu | Materialized views for P2P XML warehousing[END_REF].

View management

When a peer p d publishes a document d affecting v, p d needs to find out that v exists. To that effect, view definitions are indexed for document-driven lookup as follows. For any label (node name or word) appearing in the definition of the views v 1 , v 2 , . . . , v k , the DHT will contain a pair where the key is the label, and the value is the set of view URLs v 1 , v 2 , . . . , v k . When a peer p d publishes a document d, p d performs a lookup with all d labels (node names or words) to find a superset S a of the views that d might affect. Then, p d evaluates v(d) for each v ∈ S a . Further optimizations are discussed in [START_REF] Manolescu | Materialized views for P2P XML warehousing[END_REF]. Finally, p d sends, for each view v, the tuple set v(d) (if it is not empty) to the peer p v publishing v. Furthermore, p adds (p v , v) to a list contribT o(d) of all the peers storing views to which d has contributed.

Document d View v a (1,12) b (2,5) c (3,4) d (4,
We have so far considered that v is published before the documents which affect it. The opposite may also happen, i.e. when v is published, a document d affecting v may already exist, and v(d) needs to be added to v's extent. To that effect, we require the publisher p d of a document d to periodically look up the set of views potentially affected by d, and send v(d) to those views as described above. Thus, v will be up to date (reflecting all network documents that affect it) after the periodical check and subsequent actions have been performed by all document publishing peers.

When a peer deletes a document, messages are sent to the peers in contrib2(d), instructing them to delete the tuples of d.

Query processing

When a query q is asked on a peer p q , p first performs a look-up to identify definitions of views which may be used to rewrite q. It retrieves a set of views, and explores alternative rewritings. A rewriting is retained, which is a logical plan combining a set of views, say, v 1 @p 1 , v 2 @p 2 . . . , v k @p k . The next steps depend on the levels of the views v 1 , . . . , v k . Node level views only If all the views v 1 @p 1 , v 2 @p 2 , . . . , v k @p k are at node level, the rewriting is then transformed (optimized) into a physical executable plan, which only involves some of peers p 1 , p 2 , . . . , p k and p q . Thus, the only peers participating to the processing of a query, are peers holding views that contribute to the query rewriting, and the query peer.

For example, consider the query q = //a//b cont and the views v 1 @p 1 defined as //a id and v 2 @p 2 defined by //b id,cont . A possible rewriting is r = v 1 @p 1 ⊲⊳ a.id≺b.id v 2 @p 2 . The structural join ⊲⊳ could for instance be located at p 2 in the physical plan. Then, p 1 would send its tuples to p 2 , which will perform the join, and send the final results to p. Some document level views If some or all of the views are at document level, processing the rewriting plan only produces a list of document URIs. The respective peers are then contacted and the query is shipped to them for evaluation. Query results are to be sent directly to p.

For example, consider the query q = //a[//b]//c cont and the views v 1 @p 1 defined as //a id (node level), v 2 @p 2 defined as //b (document level), and v 3 @p 3 defined as //c id,cont (node level). A posible plan to rewrite q is: f etch(((v 1 @p 1 ⊲⊳ a.id≺c.id v 3 @p 3 ) ∩ docID v 2 @p 2 ), q)

In this expression, the ⊲⊳ identifies occurences of the //a//c pattern. We then intersect the document identifiers corresponding to these occurences, with the document identifiers of v 2 . We thus obtain the identifiers of documents which certainly feature the //a//c pattern, and some b elements, which may or may not be ancestors of an a with a c descendant. The final operator f etch(•, q) dispatches the query q to all the peers storing documents whose identifiers are provided by its input. These peers will process q and forward the results to the query peer.

Observe that one could have also used a simpler plan:

f etch(((π docID (v 1 @p 1 ) ∩ docID π docID (v 3 @p 3 )) ∩ docID v 2 @p 2 q), q)
where prior to f etch, we only intersect the document IDs of the three views. This requires less data transfers from v 1 and v 3 , however, it is less precise, as it may return more document identifiers than the previous plans, and thus potentially leads to contacting more peers than needed.

tions we make. Section 4.2 discusses view adaptation.

Assumptions

First assumption: query availability and compulsory views We make the assumption that at any time, it must be possible to answer any query P query over the peer network. This obviously assumes (i) some techniques to deal with peer failures (ViP2P uses replication to increase view availability), and (ii) tolerance for the time it takes to propagate the contribution of a newly arrived document to all the views to which it should contribute. We will not discuss these aspects further here. What matters is that there must be a way to process any query expressed in our tree pattern dialect P.

To achieve this, one may broadcast the query to all peers of the network, but this is obviously very costly. Instead, we require that all peers in the network store some compulsory views, whose size is kept to a minimum, and which allow answering more efficiently. We denote the set of compulsory views of peer p by p.comp.

As a consequence, each peer p must have a non-zero view storage budget, denoted S p .

Second assumption: peers' interest and selfish views We furthermore assume that any peer that issues a query is interested in reducing the overall processing time of the query. To that effect, peers may establish selfish views, which lead to more efficient execution strategies for the peer. Observe that the definitions of selfish views are indexed in the ViP2P network, too. Thus, they may also benefit other users (and other queries), even though they were mainly established for the interest of the peers holding them. We denote teh set of selfish views of a peer p by p.self .

Third assumption: willingness to help and collaborative views Finally, we assume that a peer is willing to devote some space to establish views if only to help the processing of other peers' queries. We denote the set of collaborative views of a peer p by p.collab.

Putting it all together, we obtain:

S p = S p,comp + S p,self + S p,collab + S p,f ree
where S p is the space budget of peer p, S p,comp is the space that p uses to store its compulsory views, S p,self is the space used to store p's selfish views, S p,collab is the space used for collaborative views, and S p,f ree is the space unused so far at peer p. Ideally, S p,f ree should be close to zero, to maximize the benefits that the storage space of p brings to this and the other network peers. When a peer joins the network, S p,comp = S p,self = S p,collab = 0 since the peer initially has no views. Upon joining, p is assigned some compulsory views and thus thus S p = S p,comp + S p,f ree .

Data statistics

We assume available for each view v, regardless of its type, its number of tuples denoted |v|. Moreover, for each document d, we assume available the number of tuples from d that belong to v and we denote this number by |v(d)|. The statistics |v| and |v d | are indexed in the network together with (as part of) the definition (metadata) of the view v. For instance, let be the view //a//b cont , then the definition of v will be indexed in the DHT by the node label a, say, at peer p xa , and by the node label b, say, at peer p xb . Then, p xa stores the association between the key a and the value consisting of the triple:

• //a//b cont (the definition of v) • |v| • ∀d ∈ D, |v(d)|
We assume such triple values inserted in the view definition index are sufficiently small not to cause performance problems. Should the set of values |v(d)| become too large, it can be compressed into a histogram structure, trading precision for space in a relatively standard way.

Query statistics We assume a given time interval named query history window and denoted hw. On each peer, for each query q that has been asked on the peer p, or to which the peer p contributed, we store:

• n hv (q), the number of times q has been asked during the time interval of length hw which ends at the current moment, c hw (q), the average cost (response time) of q during this time window and e hw (q), the effort spent by the peer in processing q during the same window

• similarly, n(q), c(q) and e(q), respectively the frequency, cost, and effort incurred to p, due to the query q.

Observe that these statistics are related to the peer and are local to the peer in the following sense: if the peer asks no query and is never solicited to participate to processing another peer's queries, the peer has no query statistics.

View utility model Given a view v, we define a utility function u(v) which aims at quantifying the cost of materializing and storing a view as well as the benefit that it would bring to the processing of a given workload (set) of queries Q = {q 1 , q 2 , . . . , q n } if it is materialized. The utility is defined by:

u(v) = n i=1 cost(q i )| ¬v - n i=1 cost(q i )| v
where, the cost(q i )| ¬v is the cost of answering a query q i given that the view v is absent and cost(q i )| v is the cost of answering the query q i in the presence of view v. A high utility value signals a view whose materialization is interesting -from the perspective of the workload Q.

View set evolution

A peer joins the network with all its space budget free, and no views. Upon joining, he is assigned a set of compulsory views. These are all document level views of the form //a, where a is the name of some XML element occuring in a D document, or //a, where a is a keyword occuring in some text node or value of a D document. A peer p is assigned a view //a such that h(a) = p where h is the hash function of the DHT. We assume that for each peer, the space budget is sufficient to store these compact compulsory views. Compulsory views are re-distributed as peers joins and leave the network as follows. Consider the compulsory view //a such that h(a) = p 1 and the peer identifier p 1 is not assigned in the network. The view will then be stored to the peer with the smallest identifier p 2 such that p 2 is larger than p 1 and the identifier p 2 is assigned. If and when the identifier p 1 is assigned later on, the view will be moved to that peer, and its URI accordingly updated in the view index, so that the view may be found at the correct peer.

The views may then evolve in time by applying one of several adaptation rules, while obeying the following constraints:

• a compulsory view is never dropped

• peers are more interested in shortening the processing time of their own queries, than in shortening the processing time of other queries

• if free space is available, peers may add collaborative views to shorten the processing of other peers' queries. Such views may be dropped later on in favor of selfish views (selfish views pre-empt space).

The adaptation process is sketched in Algorithm 1. It consists of two main procedures: the first one tries to materialize an extra view, first, for selfish reasons. A view is materialized if its utility for the peer's workload of own queries, Q self , is positive, and greated than the utility of any other possible view. Still, there may be no view recommended at this point, if e.g. the peer has no queries, or they are sufficiently well served by the existing views, or the top recommended view is larger than the available space. In this case, procedure viewAdapt will attempt similarly to materialize the best recommendation for the workload Q others .

Procedure viewDrop removes all views whose recent usage has fallen below a given threshold.

Finally, procedure adapt periodically triggers viewDrop (to see if some space can be claimed back) and then viewDrop. View wish list The algorithm outlined above has a shortcoming: empty space may go forever unused on a peer, if that peer issues no query, and it is never solicited to answer other peers' queries, either. In this case, Q self = Q others = ∅ and Algorithm 1 would not cause any changes.

To cope with such situations, we may allow each peer to build a wish list of views that may help its queries, and advertise it over the network. Wish list views are indexed just like any other views in ViP2P, but they are marked as virtual and to-be-established. The number of peers having added a given view to their wish list is globally computed. A view having exceded a given treshold of popularity is put in a special shortlist of most wanted views, and eventually, adaptation at an empty, unused peer will lead to its materialization.

Related works

An interesting recent work is [START_REF] Tang | Materialized View Selection in XML Databases[END_REF], which studies recommending XQuery views based on a set of XQuery queries. Our work is obviously related. At a superficial level, an important difference is the query language, since we consider tree patterns and not XQuery. More importantly, our views contain identifiers, based on which fragments of XML can be joined back into tree patterns, whereas identifiers are not present at the XQuery language level. Moreover, we consider document level views as a way to save space while retaining the important information. Finally, we consider view sharing in a peer-to-peer setting and focus on striking a balance between views established in a selfish purpose and those meant to help other peers process their queries.

In [START_REF] Lillis | Cooperative xpath caching[END_REF], linear XPath views are jointly maintained and exploiting in peerto-peer settings. The authors consider the situation where a group of peers collaborate to help each others' queries by establishing shared caches. There are many differences between our and that work. First, they only support navigation-based rewriting of a query based on a single view, whereas we are able to support multiple-view rewriting. Second, their work is mostly centered in simple parent-child linear XPath views, which can be organized in Trie structures due to their special simple form. In our case, a query of the form //a//b can be written based on two views //a id and //b id,cont . Obviously, there is no way of organizing such view definitions in a single view index tree, although the views may one day be used jointly.

Figure 1 :

 1 Figure 1: Sample document level views.

Figure 2 :

 2 Figure 2: A document, a node level view and the result of evaluating the view against the document.

View adaptationIn this section, we discuss how the materialized views established on each ViP2P peer are initialized, and how they evolve. Section 4.1 provides the basic assump-