Aymen Belghith
email: aymen.belghith@telecom-bretagne.eu

Loutfi Nuaymi
email: loutfi.nuaymi@enst-bretagne.fr

WiMAX capacity estimations and simulation results

In this paper, we propose some considerations for the WiMAX capacity. The developments realized for a WiMAX NS-2 module are presented. This module allows the evaluation of the WiMAX. We present the spectrum efficiency and mean sojourn time of WiMAX determined through simulations for different scheduling algorithms. It is then possible to compare theoretical values and simulation results of WiMAX spectral efficiency and highlight some interesting comments. This is done for two proposed scenarios.

I. INTRODUCTION

WiMAX is a new and powerful Broadband Wireless Access (BWA) Technology. It is based on the IEEE 802.16-2004 standard [START_REF]IEEE Standard for local and metropolitan area networks, Air Interface for Fixed Broadband Wireless Access Systems[END_REF] and its amendment 802.16e [START_REF]IEEE Standard for local and metropolitan area networks, Air Interface for Fixed Broadband Wireless Access Systems, Amendment 2: Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands and Corrigendum 1[END_REF]. It offers different tools for different environments. Many procedures and algorithms of WiMAX are not mandatory in the IEEE 802.16 standard and then represent open problems. Then, vendors and providers must choose or propose their own procedures and algorithms. The network simulation presents a solution to test the performance before applying these algorithms to the reality. Network Simulator 2 (NS-2) [START_REF]The Network[END_REF] is a widely-used tool to simulate wireless networks. Until today, this simulator does not contain a WiMAX module. Yet, there are some contributions such as the modules that are implemented by National Institute of Standards and Technology (NIST) [START_REF]Seamless and Secure Mobility[END_REF] and Network and Distributed Systems Laboratory (NDSL) [START_REF]The Design and Implementation of WiMAX module for ns-2 Simulator[END_REF].

The available features of the NIST module are Wireless-OFDM physical layer, Time Division Duplexing (TDD), management messages, Round Robin (RR) uplink scheduler, IEEE 802.16e extensions to support scanning and handovers, and fragmentation and reassembly of frames [6]. In the other hand, the available features of the NDSL module are Wireless-OFDMA physical layer, TDD, management messages, RR uplink scheduler, and Control Admission Control (CAC) mechanism [START_REF] Chen | The Design and Implementation of WiMAX Module for ns-2 Simulator[END_REF].

Since we work on the Wireless-OFDM physical layer, our NS-2 developments are based on the NIST implementation. Our contribution in this existing implementation consists of the addition and management of Quality of Service (QoS) parameters and the implementation of some scheduling algorithms. Then, we assess the scheduling methods by determining the spectrum efficiency and mean sojourn time performance measures. The mean sojourn time represents the average time a data packet spends from its generation to its delivery at the destination. Simulation results are given for two different scenarios: rural and urban scenarios. These scenarios assess scheduling methods at low and high signal-to-noise ratio (SNR) conditions, respectively. This paper is organized as follows. In Section II, we present the system model. In Section III, we introduce the WiMAX capacity as well as some considerations about the throughput and spectrum efficiency. In Section IV, we describe our proposed NS-2 module. In Section V, we present some simulation results of scheduling methods. We conclude in Section VI.

II. SYSTEM MODEL

The IEEE 802.16 standard defines the PHY and MAC layers. The PHY layer defines five physical interfaces. We consider the Orthogonal Frequency Division Multiplexing (OFDM) PHY layer in our system model. The MAC layer defines five QoS classes: Unsolicited Grant Service (UGS), real-time Polling Service (rtPS), extended real-time Polling Service (ertPS), non real-time Polling Service (nrtPS), and Best Effort (BE) QoS classes. We consider the UGS, rtPS, and BE QoS classes in our system model. Each QoS class has its mandatory QoS parameters. The main parameters of a QoS class service flow in IEEE 802.16 are summarized in Table I.

The SFID, CID, and traffic priority are mandatory for all the QoS classes. The other mandatory service flow parameters depend on the kind of the class used. For example, Maximum Sustained Traffic Rate, Maximum Latency, and Tolerate Jitter are mandatory for the UGS QoS. Maximum Sustained Traffic Rate, Maximum Sustained Traffic Rate, and Maximum Latency are mandatory for rtPS.

The BS provides radio resources for the different SS with taking into account the QoS parameters of the different service flows. Evidently, the link adaptation is useful for the BS to deliver QoS. The SNR value of a subscriber station (SS) is used to determine the MCS. The determination of the MCS depends on two values:

• The minimum entry threshold: represents the minimum SNR required to start using a more efficient MCS.

III. WIMAX CAPACITY

In this paper, we consider the OFDM PHY layer. The system capacity determines the maximum throughput that the WiMAX system can support without excessively decreasing the quality of service of the different connections. The system capacity strongly depends on the number of OFDM symbols in the frame. In the rest of this paper, a symbol is an OFDM symbol unless where mentioned. The IEEE 802.16 standard specifies that two symbols are taken for the preamble, used for synchronization, and one symbol for the Frame Control Header (FCH). The main broadcast messages are the downlink map (DL-MAP) and uplink map (UL-MAP) broadcast MAC management messages. When the BS makes the scheduling decision, it informs all the SSs, at the beginning of each frame, about his OFDM symbols allocation. This information is transmitted through the DL-MAP and UL-MAP messages, for the downlink and uplink directions, respectively. If the Modulation and Coding Scheme (MCS) used for the DL-MAP and UL-MAP is BPSK 1/2 (the most robust MCS), the size of the DL-MAP is (64 + 32 * n) / 96, and the size of UL-MAP is (56 + 48 * n) / 96, where:

• n: represents the total number of SSs that are served in the current frame (active SSs). • 96: represents the number of useful bits carried by an OFDM symbol. • 32 and 48: represent the number of bits carried by a DL-MAP Information Element (DL-MAP IE) and UL-MAP Information Element (UL-MAP IE), respectively.

Then, the total number of symbols per frame is computed. If we subtract from it the number of symbols used for the preamble, FCH, and broadcast messages, we obtain the number of symbols used for data transmission.

For the OFDM PHY, the total number of subcarriers is equal to 256 (N F T T = 256) where only 192 subcarriers are used for useful data transmission. The sampling factor, denoted fs, is equal to the nominal channel bandwidth BW multiplied by the sampling factor n.

The time duration of an OFDM symbol (T D OF DM ) can be computed as follows:

T D OF DM = useful symbol time + guard time T D OF DM = useful symbol time + G * useful symbol time T D OF DM = 1 / (one subcarrier spacing) * (1 + G) T D OF DM = [1 / (f s / N F T T )] * (1 + G) T D OF DM = [1 / (n * BW / N F T T )] * (1 + G)
Given the values of BW, n, and G, the OFDM symbol duration can be computed. With frame duration of 20 ms, channel bandwidth of 5 MHz, sampling factor of 144/125, and Cyclic Prefix (CP) ratio, denoted G, of 1/4, the OFDM symbol duration is equal to 55.5 µs and the total number of symbols is equal to 360 symbols. Those symbols are used for the preamble, FCH, broadcast messages and downlink bursts. We recall that the number of symbols used for the broadcast messages depends on the number of SSs ((64 + 32 * n) / 96 + (56 + 48 * n) / 96). Given the MCS used, G, and the number of SSs, we can compute the spectrum efficiency (see Table III).

IV. SIMULATION MODEL

Our developed module is based on the NITS implementation [START_REF]Seamless and Secure Mobility[END_REF] of the WiMAX module. The simulator used is Network Simulator (NS-2) version 2.29 and the programming language is the C++. The existing implementation contains two main modules: the PHY and MAC modules. The PHY module consists of the OFDM PHY layer with some configurable parameters such as the transmitter power, the cyclic prefix, and the frequency bandwidth. The MAC module supports the TDD mode. It also contains some configurable parameters such as the frame duration, burst modulation and contention size. In addition to the PHY and MAC modules, the existing implementation contains management messages such as the Downlink Channel Descriptor (DCD), Uplink Channel Descriptor (UCD), DL-MAP, UL-MAP, ranging request, ranging response, registration request, and registration response messages.

Our contribution consists of the addition of some QoS parameters to the service flow, the link adaptation, and some scheduling methods for the UGS, rtPS, and BE QoS classes. We also implemented unicast and contention request opportunities as defined in the standard. The main parameters of the simulation model are represented in Table IV.

A. Service Flow

The parameters of the service flows allow the BS to identify the service requirement for the associated connection. The Once the service flow parameters are initialized, the addition of a new service flow can be performed. This needs an exchange of Dynamic Service Addition (DSA) packets. These packets are defined in IEEE 802.16 and already implemented in the existing NS-2 module. There are three types of DSA packets: Dynamic Service Addition Request (DSA-REQ), Dynamic Service Addition Response (DSA-RSP), and Dynamic Service Addition Acknowledgment (DSA-ACK). These packets are used in order to create a new service flow between an SS and a BS.

Since the existing implementation of the DSA-REQ and DSA-RSP packets does not contain the service flow parameter, we add this parameter to the packets and therefore the sizes of these packets are modified. The added service flow parameter contains the following parameters: the SFID, Service Flow Scheduling Type, CID, Traffic Priority, Maximum Sustained Traffic Rate, Minimum Reserved Traffic Rate, Tolerated Jitter, and Maximum Latency parameters. In addition to the modification of the service flow parameter of the DSA-REQ and DSA-RSP packets, we need to add some instructions:

• When a DSA-REQ packet is sent, the flow service parameter is added to this packet as defined in the IEEE 802.16 standard.

• When a DSA-REQ packet is received, the service flow and QoS parameters of the created data connection are filled up from the service flow parameter of the received DSA-REQ packet. Then, a value of the CID parameter of the service flow is generated and assigned. • When a DSA-RSP packet is sent, the service flow parameter is added to this packet. When a DSA-RSP packet is received, the service flow and QoS parameters of the created data connection are filled up from the service flow parameter of the received DSA-RSP packet.

B. Link Adaptation

The existing implementation does not take into account the SNR values and all the subscribers use a same MCS. The default value of the used MCS is BPSK . To provide the possibility of using different modulation and coding schemes, the BS must know the SNR values of the different subscribers. The SNR value can change during the simulation and therefore the subscribers can use different MCS. The used MCS is determined from the values of SNR which are defined by the IEEE 802.16e standard.

C. Base Station Uplink Scheduling

The existing implementation does not differentiate between the different QoS classes. The scheduling algorithm of the existing implementation is described as follows. After taking sufficient number of symbols to send its packets, the BS reserves the rest of symbols for a single station, during the whole frame, using the RR scheduler. Thus, at each frame, at most one subscriber can send its packets independently of the QoS classes. The implemented scheduling algorithm has to be changed in order to differentiate between the QoS classes and take into account the QoS parameters. In this paper, we consider only three of them: UGS, rtPS and BE QoS classes.

1) Scheduling for UGS QoS Class: The proposed UGS scheduler is described as follows. The BS determines all the subscriber stations that have UGS connections. For each UGS connection, the BS determines the transmission time using the Maximum Sustained Traffic Rate parameter. Then, the BS determines the number of symbols to be reserved using the determined transmission time and MCS used values. The available symbols must be sufficient to serve all the UGS connections. Once the number of symbols to allocate is determined, the BS updates the UL-MAP message and adds a new uplink burst.

2) Scheduling for rtPS QoS Class: The rtPS scheduling consists of two parts. The BS periodically provides unicast request opportunities. When the SS receives an unicast request polling, it sends a bandwidth request. The bandwidth request contains the length of its uplink data connection queue. We assume that subscribers are disciplined and they use these grants to only send bandwidth requests.

On the other hand, the BS provides resources to the rtPS subscribers using the received bandwidth requests. The BS performs a scheduling algorithm to determine the rtPS connections to serve. Then, it determines the number of symbols to be reserved. The BS allocates the remaining symbols if there are not enough radio resources. After each allocation, the BS updates the bandwidth to reserve in the following frames.

In this paper, we focus on the rtPS schedulers and implement some of them in our NS-2 module. The implemented schedulers are the RR, maximum Signal-to-Interference (mSIR), Weighted Round Robin (WRR), and Temporary Removal Scheduler (TRS) schedulers. We briefly describe these schedulers. The RR scheduler equitably distributes channel resources to all the SSs. The mSIR scheduler allocates radio resources to SSs that have the highest SNR. The WRR scheduler is an extension of the RR scheduler and based on static weights. The TRS scheduler [START_REF] Ball | Performance Analysis of Temporary Removal Scheduling applied to mobile WiMAX Scenarios in Tight Frequency Reuse[END_REF] temporarily blocks SSs having SNR smaller than a defined threshold. We combine the TRS scheduler with the RR and mSIR schedulers (called TRS+RR and TRS+mSIR, respectively). The TRS+RR scheduler reserves 1/k of the whole radio resources if there are k SSs to schedule. While the TRS+mSIR reserves the whole radio resources for SSs that have the highest SNR.

3) Scheduling for BE QoS Class: The BE scheduling consists of two parts. The BS provides contention request opportunities at the beginning of each uplink subframe. Periodically, an SS uses the contention request opportunities to send, with contention, a bandwidth request that contains the length of its uplink data connection queue.

On the other hand, the BS provides resources to the BE subscribers using the received bandwidth requests. The BS performs the RR scheduler to determine the BE connections to serve. Then, it verifies if the SS has a bandwidth request. If it has not, the BS checks the next SS. Otherwise, the BS determines the transmission time and the number of symbols to be reserved. If there are not enough radio resources, the BS only allocates the remaining symbols and updates the bandwidth to reserve during the following frames.

V. SIMULATION RESULTS

A. Rural Scenario

In the rural scenario, we assume that the subscribers use the QPSK 1/2, QPSK 3/4, or 16QAM 1/2 MCSs. There are nine UGS connections, nine rtPS connections, and two BE connections. In this section, we study the behavior of some rtPS schedulers in such SNR conditions. Fig. 1 shows the spectrum efficiency as a function of the traffic load submitted to the network. This figure shows that the spectrum efficiency is between 0.7 bit/s/Hz (for the RR scheduler) and 0.93 bit/s/Hz (for the mSIR scheduler). We observe that the TRS+mSIR scheduler is less efficient than the mSIR scheduler. This is because the TRS+mSIR scheduler may temporarily block the traffic of the SSs having small SNR even if there are remaining symbols for data frame transmissions.

We also note that the WRR and TRS+RR schedulers outperform the RR scheduler. This is due to the taking into account the SNR of the different subscribers. Indeed, the WRR scheduler assigns high weights to the SSs having higher SNR. On the other hand, the TRS+RR scheduler temporary blocks the SSs having small SNR.

The mean sojourn time is shown on Fig. 2. We point out that the mean sojourn time represents a vital parameter for real applications. We interestingly note that the mSIR and TRS+mSIR schedulers require a large average delay to deliver data frames. This is due to the traffic freeze of the SSs having small SNR. We observe that the three others schedulers exhibit a mean sojourn time less than 20 s even if the networks is overloaded. This is because these schedulers do not block any connection independently of its SNR.

B. Urban Scenario

In the urban scenario, we assume that the subscribers use the 16QAM 3/4, 64QAM 2/3, or 64QAM 3/4 MCSs. There In this section, we study the behaviour of some schedulers in such SNR conditions. Fig. 3 depicts the spectrum efficiency as a function of the traffic load. This figure shows that the spectrum efficiency of the five schedulers is between 1.71 bit/s/Hz (for the TRS+RR scheduler) and 2.03 bit/s/Hz (for the mSIR and TRS+mSIR schedulers). We note that the RR scheduler, with spectrum efficiency equal to 1.79 bit/s/Hz, outperforms the TRS+RR scheduler. Indeed, the TRS+RR scheduler does not block any SS because of the high SNR values of all the subscribers. Moreover, since a preamble is added to each uplink burst, the BS schedules less useful symbols when it serves more SSs per frame.

We also observe that the WRR scheduler, with spectrum efficiency equal to 1.95 bit/s/Hz, outperforms the RR and TRS+RR schedulers. This is due to the taking into account the MCSs used by the different SSs.

The mean sojourn time of the five schedulers is shown in Fig. 4. As the mSIR and TRS+mSIR schedulers block the traffic of the SSs having small SNR, we observe that the mean sojourn of these schedulers is very high.

We also note that the three other schedulers exhibit a mean sojourn time less than 6.5 s. The RR and TRS+RR schedulers slightly outperforms the WRR scheduler. This is because the complete cycle of the WRR scheduler is longer than that of the RR and TRS+RR schedulers.

VI. CONCLUSION

In this paper, we considered the capacity and spectrum efficiency of WiMAX. We consider both simple analytical computations and NS-2 simulations. Evidently, WiMAX capacity is completely dependent of the scenario (the environment) and the scheduling algorithm. The mSIR and TRS+mSIR schedulers provide the highest spectrum efficiency at low and high SNR conditions (0.93 bit/s/Hz and 2.03 bit/s/Hz, respectively). The RR, WRR, and TRS+RR schedulers provide mean sojourn time smaller than 6.5 s and 20 s at high and low SNR conditions, respectively. The WRR scheduler outperforms the RR and TRS+RR schedulers with spectrum efficiency equal to 0.8 bit/s/Hz and 1.95 bit/s/Hz at low and high SNR conditions, respectively. At high SNR conditions, the mSIR and TRS+mSIR schedulers slightly outperform the WRR scheduler with a difference between spectrum efficiency values equal to 0.08 bit/s/Hz while this difference is almost the double at low SNR conditions.

Our results are obtained for an environment where all the available bandwidth is used in every cell of the network. Yet, it is now well-known that a reuse factor of the order of 3 is needed (see, e.g., [START_REF] Ntagkounakis | Cost-efficient WiMAX Network deployment: the hybrid Outdoor/Indoor dual-layer coverage approach[END_REF]) if intelligent antennas techniques such as MIMO (Multiple-Input, Multiple-Output) and smart antennas are not used. Then, our figures represent rather optimistic values if intelligent antennas techniques are not applied. As future research, we intend to study WiMAX capacity for other scheduling algorithms and other environments.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Spectrum efficiency versus traffic load

Fig. 3 .Fig. 4 .

 34 Fig. 3. Spectrum efficiency versus traffic load

ACKNOWLEDGMENT

This work is supported by the Britanny (Bretagne) Region in the framework of Op WiMAX Project.


Brigitte Camillieri

Marie-Ange Bueno
email: marie-ange.bueno@uha.fr

Marie Fabre

Benjamin Juan

Betty Lemaire-Semail

Laurence Mouchnino

From finger friction and induced vibrations to brain activation: tactile comparison between real and virtual textile fabrics

Keywords: Tactile, friction, finger, textile, virtual surface, EEG

The objective is to compare the tactile rendering of real and virtual textile surfaces. A grooved woven (twill) and a hairy fabric (velvet) were studied. The virtual fabrics were simulated with a tactile device. The comparison was done by measuring the finger interaction in terms of coefficient of friction (COF) and induced vibrations, and brain activation by electroencephalography (EEG). EEG showed that the real and virtual twill fabrics are close, contrary to real and virtual velvets. The finger friction showed that for both fabrics the rendering of virtual compared to real fabrics is very good in terms of COF, low in terms of finger induced vibrations in high frequencies, but differs for the velvet texture for low frequencies.

INTRODUCTION

The possibility to simulate the touch feeling of surfaces is of high importance for many applications: e-commerce for products in direct interaction with humans (garments, car upholstery and dashboard, furniture …) [START_REF] Khakimdjanova | Online visual merchandising practice of apparel e-merchants[END_REF], virtual prototyping as design assistance [START_REF] Fontana | Physics-based Modelling and Simulation of Functional Cloth for Virtual Prototyping Applications[END_REF], and also tactile deficiency detection and patient rehabilitation.

In the textile field, tactile simulation could be used by the final consumer to choose a textile material sold through the internet [START_REF] Khakimdjanova | Online visual merchandising practice of apparel e-merchants[END_REF][START_REF] Bingi | The Challenges Facing Global E-commerce: A Multidimensional Perspective[END_REF][START_REF] Peck | To Have and To Hold:The Influence of Haptic Information on Product Judgments[END_REF][START_REF] Varadarajan | Marketing Strategy and the Internet: An Organizing Framework[END_REF]. In the near future, it might be common to have one's own 3D body shape [START_REF] Loker | Dress in the Third Dimension: Online Interactivity and Its New Horizons[END_REF], to choose a fabric in terms of colour, texture and drape, to choose a garment shape and to simulate individual avatars wearing virtual garments [START_REF] Fontana | Physics-based Modelling and Simulation of Functional Cloth for Virtual Prototyping Applications[END_REF][START_REF] Luginbühl | Towards the Automatic Generation of 3D Photo-Realistic Avatars Using 3D Scanned Data[END_REF]. In pursuing these goals it is therefore essential to improve the touch rendering of the virtual fabrics [START_REF] Cano | The influence of image interactivity upon user engagement when using mobile touch screens[END_REF]. In this field, few papers report simulation of textile fabrics with a tactile device. The tactile device used can be a friction modulation device based on ultrasonic vibration [START_REF] Maeno | Tactile Display of Surface Texture by use of Amplitude Modulation of Ultrasonic Vibration[END_REF] or an array of 256 pin-electrodes allowing lateral finger movement [START_REF] Peruzzini | Electro-tactile device for texture simulation[END_REF]. In both cases, the control signal is generated from the surface textile modelled by its surface microgeometry. Therefore, the adhesion or deformation of the surface, i.e. the friction behaviour, is not taken into account.

One's ability to perceive different fabrics involves both cortical and peripheral mechanisms.

The tactile afferents from the finger signal the transformation of soft tissues that occurs when the fingers interact with objects and thus provide information about the physical properties of the fabrics and the contact between the fabric and the finger. The brain uses the tactile afferent information related for example to the friction between contacted fabrics and the digits to categorise the fabric. Categorisation is the process by which sensory stimuli are recognised, differentiated, and placed into groups. Through this cognitive process the physical properties of the stimuli are transformed into knowledge of the fabric under the digits. But it is not known how, or even whether, the perception of virtual stimuli is modified during movement exploration.

The literature reported results about friction between human finger or skin and textile fabrics [START_REF] Darden | Investigation of skin tribology and its effects on the tactile attributes of polymer fabrics[END_REF][START_REF] Derler | Tribology of human skin and mechanical skin equivalents in contact with textiles[END_REF][START_REF] Gerhardt | Influence of epidermal hydration on the friction of human skin against textiles[END_REF][START_REF] Kenins | Influence of Fiber Type and Moisture on Measured Fabric-to-Skin Friction[END_REF][START_REF] Ramalho | Friction and tactile perception of textiles fabrics[END_REF]. Most of them used the coefficient of friction (COF). Nevertheless it is known since more than an half century that the COF is necessary but not sufficient to characterise fabric touch [START_REF] Morrow | The frictional properties of cotton materials[END_REF][START_REF] Dreby | A Friction Meter for Determining the Coefficient of Kinetic Friction of Fabrics[END_REF][START_REF] Hoffman | Some Relations of Fiber Properties to Fabric Hand[END_REF], therefore it can be supposed it is not sufficient for simulating fabric touch. More recently, from the consideration of the duplex tactile theory of tactile texture perception, some studies consider finger induced vibrations from tactile surfaces [START_REF] Fagiani | Tactile perception by friction induced vibrations[END_REF][START_REF] Fagiani | Contact of a finger on rigid surfaces and textiles: Friction coefficient and induced vibrations[END_REF][START_REF] Zahouani | Effect of roughness on vibration of human finger during a friction test[END_REF]. For a given fabric a specific spectrum can be obtained [START_REF] Fagiani | Tactile perception by friction induced vibrations[END_REF][START_REF] Fagiani | Contact of a finger on rigid surfaces and textiles: Friction coefficient and induced vibrations[END_REF].

Few papers reported studies of fabric touch with electroencephalography (EEG) and none on virtual textures. The tactile comfort during clothing wear has been evaluated with EEG, and it was observed the higher the shirt mass density, the higher the energy percentages at both the left and right occipitalia [START_REF] Wang | Experimental Study of Clothing Tactile Comfort Based on Electro-neurophysiology[END_REF]. Recently, the COF between human fingers and textile fabrics, induced vibrations from an artificial finger and perception in terms of different descriptors (rough-smooth, coarse-fine, complex-uniform and surface comfort), have been correlated with EEG results [START_REF] Chen | Experimental research on the tactile perception from fingertip skin friction[END_REF]. It is quite difficult to extract results in a textile material point of view because the textile surfaces used are not precisely described. Specifically the weave pattern is not indicated. Nevertheless, the descriptors used are linearly correlated with the COF which is probably due to the choice of the fabrics investigated. In fact, the most influential parameter is the size of the elementary mesh linked to the number of warp and weft yarns per centimetre and the yarn count. The silk fabric is probably the smoothest, and it reveals a higher real contact area. Moreover, the direction of movement, i.e. in the warp or weft direction, is not indicated.

It seems the movement is anteroposterior.

In a previous study [START_REF] Messaoud | Design and Control of a Tactile Stimulator for Real Texture Simulation: Application to Textile Fabrics[END_REF][START_REF] Messaoud | Textile Fabrics' Texture: From Multi-level Feature Extraction to Tactile Simulation[END_REF], three very different fabrics have been simulated from a tactile stimulator named STIMTAC. The objective was to show if the human participants were able to associate the virtual fabric to the corresponding real fabric. The results obtained showed in 80% of cases a virtual fabric has been associated to the correct real fabric [START_REF] Messaoud | Design and Control of a Tactile Stimulator for Real Texture Simulation: Application to Textile Fabrics[END_REF]. Nevertheless, the distance between the real and the virtual fabrics has not been evaluated. The goal of this paper is to compare finger behaviour and cortical responses during a tactile task in a lateral finger movement for real or virtual fabrics, in terms of finger friction, induced vibrations and brain activation measured with EEG. The idea is to use further the analysis of the differences between virtual and real surfaces to improve the design and control of the tactile simulators.

The paper is organised as following: first, the experimental apparatus and methods both for tribological and EEG measurements are described; then the results are shown, highlighting the differences between virtual and real surfaces for two kinds of fabrics. Last, the discussion gives a first analysis and explanation of these differences.

MATERIALS AND METHODS

Real and virtual textile fabrics

Two fabrics have been investigated: a twill woven fabric and a velvet knitted fabric. The twill fabric is obtained by interlacing two yarns in the plane of the fabric in two orthogonal directions. This fabric is rather compact with 44 warp and 37 weft threads per centimetre. The yarns consist of filaments (97% polyethylene terephthalate, i.e. PET, and 3% elastane), therefore the surface hairiness is very weak. The yarn fineness is 26 tex (1 tex = 1 g/km). The intercrossing of the yarns generates a fabric with relief in the form of inclined ribs (19.5 ribs or grooves/cm) (Fig. 1a-b).

The second fabric is very hairy and is obtained by knitting a ground yarn (in PET) forming the knitted structure, with some acrylic fibres introduced in the ground structure during the loop formation in order to form bristles/plush yarns (Fig. 1c). The acrylic fibres are shaved at a fixed length when they are caught in the knitted structure. The released bristles make up the pile and are in the form of fibre bundles held on one side of the structure. The bristles obtained are parallel and of equal length (about 2 mm). For this fabric which will be named velvet afterwards, the pile has a preferred direction in which it lies down, as with the fur of an animal. This preferred direction is called the "along pile" direction while the opposite direction is the "against pile" direction.

The virtual textile fabrics are simulated from the tactile device STIMTAC from a method described elsewhere [START_REF] Messaoud | Design and Control of a Tactile Stimulator for Real Texture Simulation: Application to Textile Fabrics[END_REF][START_REF] Messaoud | Textile Fabrics' Texture: From Multi-level Feature Extraction to Tactile Simulation[END_REF][START_REF] Bueno | Pile surface tactile simulation: role of the slider shape, texture close to fingerprints and the joint-stiffness[END_REF]. STIMTAC is a continuous tactile stimulator and looks like the touchpad of a laptop computer (Fig. 2). STIMTAC provides a constant stimulation all over the touched surface at a given time. It is based on the reduction of the COF which is obtained with ultrasonic vibrations (30-40 kHz) of the touched plate forming an air gap acting like a lubricant.

The frequency of vibration of the plate is too high to be perceptible by the human hand which cannot perceive vibrations higher than 1 kHz [START_REF]Ch 17 : The sense of touch: Performance and peripheral neural process[END_REF][START_REF] Morley | Perceived pith of vibrotactile stimuli: Effects of vibration amplitude, and implications for vibration frequency coding[END_REF]. The measurement of the finger position allows to change the plate vibration amplitude, i.e. the COF, every 0.1s (100 Hz). The simulation protocol of the investigated fabrics, i.e. the twill and the velvet fabrics, has been described elsewhere [START_REF] Messaoud | Design and Control of a Tactile Stimulator for Real Texture Simulation: Application to Textile Fabrics[END_REF][START_REF] Messaoud | Textile Fabrics' Texture: From Multi-level Feature Extraction to Tactile Simulation[END_REF]. The friction signal obtained from the considered fabrics and specific sliders has been recorded. The instantaneous COF is obtained for each surface and used for the command signal of STIMTAC for a given virtual fabric [START_REF] Cornuault | Influence of the physicochemical, mechanical and morphological fingerpad's properties on the frictional distinction of sticky/slippery surfaces[END_REF][START_REF] Messaoud | Relation between human perceived friction and finger friction characteristics[END_REF]. The surface of the samples (real as virtual) was 80×50 mm 2 .

Participants and tasks

Nine right-handed participants without any known neurological, physiological, cognitive and motor disorders (4 women and 5 men) participated in the experiment (28 to 57 years with an average of 44). All procedures performed were in accordance with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. The participants gave informed consent and provided information about their date of birth. None of them had been subjected to a similar experiment before.

Each participant was requested to follow the same experiment procedure during approximately 1.5 hours. This procedure was chronologically organised as follows. The subject washed and dried her/his hands. The experiment took place in a room whose atmosphere was conditioned (202°C and 655% of relative humidity). Participants were seated in front of the tribometer (see §2.3). To ensure a correct position and comfort, an adjustable support covered with a towel held the subject's right arm (Fig. 2a). Participants were asked to close their eyes upon receiving the verbal instructions on the nature of the upcoming task while a metronome with beats set at 1 Hz (60 beats/min) was played. The instructions indicated static or medio-lateral movement tasks for the different fabrics. In this task, the participants were asked to move back and forth during 32 seconds at the speed of the metronome and to focus on the material they were rubbing.

They were instructed to move their finger at an inclination angle of 25 degrees (between the finger and the surface). The movement amplitude was set at 40 mm, the mean velocity at 40 mm/s and the normal force at 0.5 N. Before the experimental session, a training session with the eyes opened was performed on a fabric different from those used in the experiment, allowing the participants to adjust the amplitude of the movement of his/her finger and the normal force through a visual feedback on a computer screen showing the applied load. In all movement tasks, the participants heard a 50 ms tone (i.e., go signal for starting movement execution) delivered 3 seconds after the onset of the recording session (Fig. 3). Moreover a static control task was performed: the participants were instructed to remain still throughout the trials, with the finger on the investigated surface. For reasons of homogeneity, the same auditory cues (i.e., go signal and metronome beats) as in the movement tasks were also delivered.

Virtual and real fabrics were tested with a lateral finger movement. The twill fabric has ribs and the finger always moves perpendicular to the ribs. The velvet fabric has been tested with a finger movement along (i.e., rightward direction) and against (i.e., leftward direction) main pile directions (Fig. 1c). Therefore, four measurements have been processed for the real velvet and four for the virtual velvet, and the same for the twill, i.e. a total of sixteen measurements.

Between each measurement, an operator put a new sample in a random order and placed the finger at the starting point.

Tribological measurements: Finger friction and induced vibrations

To measure the friction between the finger and the fabric, a three-axis load cell (model 3A60-20N, Interface Inc., Scottsdale, Arizona) was used. It provided the components of the force exerted by the finger along three orthogonal axes (the vertical axis = normal force; the axes in the horizontal plane gave the tangential force). The real fabric or the STIMTAC were positioned directly on the load cell (Fig. 2b).

The data were acquired with Pulse software from Bruël & Kjaer, and the forces were calculated by an Excel spreadsheet. The procedure to obtain the COF is summarised in Fig. 4. The tangential force was calculated from its components in the horizontal plane (Ftx and Fty) which give the COF, ratio of the tangential force Ft to the normal force Fn. During a finger movement, the friction force, and therefore the COF, is respectively positive for the rightward movement and negative for the leftward direction. The values in the transient (when reversing the direction of motion) are ignored. The COF values between a minimum value and a maximum value determined from the plot have been retained. The COF in each of the directions of movement of the finger was obtained, and then the mean value was considered.

The vertical vibrations of the finger were measured by an accelerometer (Piezoelectric Charge

Accelerometer 4374 with a charge amplifier 2635 from Bruël & Kjaer, Mennecy, France). It was stuck on the right forefinger at 3 mm above the nail.

The accelerometer signal is analysed in the frequency domain and the whole process by the spectrum analyser Pulse. The autospectrum is calculated; it is the average of several spectra, i.e. 10 spectra in this study. The root mean square of the acceleration is considered relative to frequency.

The parameter extracted from the autospectrum is the power P for a frequency bandwidth: Whatever the fabric, twill or velvet, virtual or real and the participant, the total frequency bandwidth is taken from 0 to 1000 Hz. Because the finger is sensitive between about 3 to 1000 Hz [START_REF]Ch 17 : The sense of touch: Performance and peripheral neural process[END_REF], the low frequencies under 3 Hz are not considered.

    C f RMS f P f     2 (1)

Electroencephalography recordings and analysis

Electroencephalographic (EEG) activity was recorded continuously from 64 Ag/AgCl surface electrodes embedded in an elastic cap (BioSemi ActiveTwo system, BioSemi, Netherlands). Specific to the BioSemi system, "ground" electrodes were replaced by Common Mode Sense EEG signals were obtained by averaging, for each participant and each task (static and lateral movement tasks) and condition (virtual and real velvet or twill), all epochs synchronised relative to the movement onset in the leftward direction. Forty leftward movements were averaged. The leftward direction was preferred because in active touch the human finger moves with the inner part of the finger (i.e., in a leftward direction for movement with the right hand) which is exquisitely sensitive in perceiving different materials. This was observed by the authors in different studies. The average amplitude of the 50-ms pre-epoch served as baseline.

The neural sources of the exploring movement were estimated using the dynamical Statistical Parametric Mapping (dSPM) [START_REF] Dale | Dynamic Statistical Parametric Mapping: Combining fMRI and MEG for High-Resolution Imaging of Cortical Activity[END_REF] implemented in the Brainstorm software [START_REF] Tadel | Brainstorm: a user-friendly application for MEG/EEG analysis[END_REF] (freely available at http://neuroimage.usc.edu/brainstorm). The data from all sensors processed and averaged for each participant, condition and electrode were considered. The forward model was computed using a three-shell sphere boundary element model (BEM) on the anatomical MRI brain MNI Colin27 template (15000 vertices), a predominant volume conductor model [START_REF] Huang | The New York Head-A precise standardized volume conductor model for EEG source localization and tES targeting[END_REF][START_REF] Mosher | EEG and MEG: forward solutions for inverse methods[END_REF].

Statistic data treatment

All the tribological results are expressed as mean ± one standard deviation. The data treatment has been done with the software XLSTAT. The objective was to compare two sets of data in order to know if they are extracted from the same population or not. In all the cases, the data from the two sets are obtained from the same participant, therefore they are paired. Firstly, each set of data has been verified to follow the normal law with the Shapiro-Wilk test (p-value>0.05).

If the two sets follow the normal law, the variances were compared with the Fisher-Snedecor test (F-test). In all these cases for which the variances were not significantly different, the means have been compared with the Student's t-test for paired data. If one or both of the two sets don't verify the normal law, the Wilcoxon signed rank test for paired data has been used. In order to test the linear correlation between two sets of data, the Pearson's coefficient of correlation R is calculated, and its square R², the coefficient of determination, is used in demonstrating the linear correlation's strength in terms of percentage. For EEG measurement, the paired t-test has been used for the statistical source estimation maps for contrasts for each fabric (velvet and twill)

[real minus virtual].

RESULTS

General comments on COF and induced vibrations

For a given participant, the four measurements done are quite reproducible. However, it is observed the COF varies substantially from person to person. This is in accordance with previous results obtained for both real textile surfaces [START_REF] Camillieri | Artificial finger design for investigating the tactile friction of textile surfaces[END_REF] and virtual surfaces simulated by STIMTAC [START_REF] Cornuault | Influence of the physicochemical, mechanical and morphological fingerpad's properties on the frictional distinction of sticky/slippery surfaces[END_REF][START_REF] Messaoud | Relation between human perceived friction and finger friction characteristics[END_REF]. In fact, the COF between the finger and a surface depends on the hydrolipid film composition, in terms of water and lipid ratio, especially with a smooth surface as STIMTAC [START_REF] Cornuault | Influence of the physicochemical, mechanical and morphological fingerpad's properties on the frictional distinction of sticky/slippery surfaces[END_REF]. This variation cannot be attributed to the environment in terms of temperature and relative humidity because the measurements are done in controlled atmosphere (see section 2.2).

Moreover, for a given surface, some similarities can be identified between the autospectra obtained from the whole panel of participants.

For all the participants and for the real and virtual velvet fabrics, the interesting frequency bandwidths are from 3 to 100 Hz and from 100 to 400 Hz (Fig. 5). The real twill fabric gives two types of autospectra depending on the participant (Fig. 6a-b). The first type of autospectra (Fig. 6a) has two interesting bandwidths and [200-400 Hz]. The second type presents a frequency lower than 100 Hz (Fig. 6b). For the virtual twill fabric (Fig. 6c), the autospectra present two interesting frequency bandwidths, i.e. and [200-400 Hz].

For the twill woven fabric, the spatial period between the ribs is close to 0.5 mm (see §2.1), giving a frequency of around 80 Hz. In most cases the peak frequency in the bandwidth [3-200 Hz] has a maximum less than 100 Hz, probably due to the fabric relief. For the velvet fabric, the specific spatial length is due to hair tuft with a value of around 1 mm, giving a frequency of about 40 Hz which corresponds approximately to the max of the peak between [3-100 Hz]. These results are in accordance with [START_REF] Fagiani | Tactile perception by friction induced vibrations[END_REF][START_REF] Fagiani | Contact of a finger on rigid surfaces and textiles: Friction coefficient and induced vibrations[END_REF].

Comparison between real and virtual velvet fabrics

The statistical analysis reveals the COF for virtual and real velvet can be considered to originate from the same population (p-value=0.10 for α=0.05). Fig. 7 highlights the correlation between virtual and real velvet depending on the participants. The coefficient R² is 0.87 which is very good. However, for some participants it can be observed that with virtual velvet the standard deviation is higher than with real surfaces. Moreover, the range of COF is wider for virtual velvet with [0.1, 1.2] than for real velvet with [0.4, 0.9].

For the finger induced vibration analysis, for the different bandwidths [3-1000 Hz], and [100-400 Hz], the power data obtained for the real and the virtual velvet fabrics have been compared (Fig. 8). The powers for the frequencies [3-1000 Hz] and [3-100 Hz] can be considered to originate from the same population (p-value respectively 0.43 and 0.81, for α=0.05) for both real and virtual fabrics. Nevertheless, the coefficients R² are close to zero with 0.04 for [3-1000 Hz] and 0.08 for [3-100 Hz]. On the contrary, for the powers for the frequencies [100-400 Hz] the p-value is close to zero (0.04 for α=0.05), indicating that the two distributions did not originate from the same population.

The powers in the two frequency bandwidths [3-100 Hz] and [100-400 Hz] have been compared for both real and virtual velvet fabrics (Fig. 9) to confirm that each bandwidth was independent and therefore can be processed separately in our analyses. As expected, there is no obvious correlation between these two bandwidths. The data range in the bandwidth has the same width for both real and virtual fabrics and is around [0.2-0.8], but for [100-400 Hz] the data range is wider for the virtual fabric than for the real velvet fabric.

To highlight the possible difference in brain activity that leads to a bias in the perception of the fabric for the virtual velvet, the statistical source maps were computed for each task and fabric (Fig. 10). The maps were previously averaged minus the static control task. For the velvet fabric, some differences between real and virtual fabrics were observed. The statistical source maps revealed that the activity of the left orbitofrontal cortex together with the left posterior parietal cortex (PPC) and the dorsolateral prefrontal cortices (dl-PFC) of both hemispheres were greater when participants moved their finger on the virtual fabric than on the real velvet fabric.

Comparison between real and virtual twill fabrics

The COF for virtual and real twill fabrics can be considered to originate from the same population (p-value=0.10 for α=0.05), and R² is 0.93 (Fig. 11). As for velvet, the range of both COF is wider for virtual than for real twill fabric.

For the finger induced vibration analysis, for the different bandwidths [3-1000 Hz], and [200-400 Hz], the power data obtained for the real and the virtual twill fabrics have been compared (Fig. 12). The powers for the frequencies [3-1000 Hz] and can be considered to originate from the same population (p-value respectively 1.0 and 0.73 for α=0.05) for both real and virtual fabrics. The coefficients R² are only average with 0.42 for [3-1000 Hz] and 0.50 for . On the contrary, for the powers for [200-400 Hz] the p-value is close to zero (0.001 for α=0.05), indicating that the two distributions did not originate from the same population.

The powers in the two frequency bandwidths and [200-400 Hz] have been compared for both real and virtual twill fabrics (Fig. 13) to confirm that each bandwidth was independent and therefore can be processed separately in our analyses. There is no correlation between these two bandwidths.

The brain activity associated with a close perception for both real and virtual twill fabrics is shown in Fig. 14. The statistical source maps revealed that the activity of the left frontopolar PFC and the anterior premotor cortex were greater when participants moved on a virtual fabric than on the real twill.

DISCUSSION

The results obtained are synthesised in Table 1.

Each surface can be considered to give its own signature in terms of COF and vibration as well as brain activity. These signatures could explain the way the sensory stimuli are categorised to belong to the same fabric or not by the participants.

First of all, in this study it is confirmed that the COF was not sufficient for simulating fabric touch. Indeed, the high COF correlations between the real and virtual fabrics during lateral movement (for the velvet, R 2 =0.87 and for the twill, R 2 =0.93) were associated with different signatures in terms of frequency bands and brain activity. But some distance between the real and the virtual fabrics reported in this study could account for differences in the perception of the virtual fabrics relative to the real ones. For the finger vibration induced from friction, the powers in the perception range of the finger [3-1000 Hz] are considered to be extracted from the same population between the real and the virtual fabrics whatever the fabric, velvet (p-value of 0.43) or twill (p-value of 1.0). For the twill fabric, there is an average linear correlation between real and virtual fabrics (R²=0.42) which was not observed for the velvet (R²=0.04).

Therefore, on the whole bandwidth, the power of the friction induced vibrations can be considered to be satisfactory for twill fabric and should be improved for velvet. However, an analysis on the whole frequency bandwidth is not sufficient. Some differences were highlighted with a deeper analysis from the identified frequency bandwidths for each fabric. Two frequency bands were reported for all the fabrics. In the lower range of frequencies ([3-100 Hz] and for the velvet and twill respectively), the powers for the real and the virtual fabrics were extracted from the same population as confirmed the p-values (0.81 and 0.73 for the velvet and twill respectively). The simulation at these frequencies can be considered as satisfactory to the exception that the correspondence between the real and the virtual for the velvet fabric failed to be relevant (R 2 =0.08) as compared to the twill (R 2 =0.50).

A striking result was observed for the highest frequency bandwidth ([100-400 Hz] or [200-400 Hz] for the velvet and twill respectively) in that the powers of the real and the virtual fabrics are not extracted from the same population (p-values close to zero), likely due to the clear presence of this highest bandwidth for the virtual fabrics and not for the real ones (Fig. 5 and6). These results show that the velvet and twill simulations have to be improved in the highest frequency bandwidths.

Overall the frequency band analysis pointed out the lower range of frequencies [3-100 Hz] in the velvet as a candidate for the wrong perception for the virtual velvet fabric. In fact, the virtual velvet was not categorised by the participants as being close to a velvet fabric. Indeed, the [3-100 Hz] induced vibrations when the finger interacts with the real or virtual fabric stimulated differently the tactile afferents that innervate the finger. Among the tactile afferents, the FA-II (fast-adapting type II) Meissner endings sensitive to dynamic skin deformation of relatively high frequency (~5-50 Hz) and Pacinian endings extremely sensitive to mechanical transients and high frequency vibrations (~40-400 Hz) could be stimulated by this [3-100 Hz] bandwidth propagating through biological tissues [START_REF] Johansson | Coding and use of tactile signals from the fingertips in object manipulation tasks[END_REF]. It can be noticed that the peak frequency [START_REF] Messaoud | Relation between human perceived friction and finger friction characteristics[END_REF][START_REF] Dale | Dynamic Statistical Parametric Mapping: Combining fMRI and MEG for High-Resolution Imaging of Cortical Activity[END_REF][START_REF] Tadel | Brainstorm: a user-friendly application for MEG/EEG analysis[END_REF][START_REF] Huang | The New York Head-A precise standardized volume conductor model for EEG source localization and tES targeting[END_REF][START_REF] Mosher | EEG and MEG: forward solutions for inverse methods[END_REF][START_REF] Camillieri | Artificial finger design for investigating the tactile friction of textile surfaces[END_REF][START_REF] Johansson | Coding and use of tactile signals from the fingertips in object manipulation tasks[END_REF][START_REF] Mountcastle | Cortical neuronal mechanisms in fluttervibration studied in unanesthetized monkeys. Neuronal periodicity and frequency discrimination[END_REF][START_REF] Condon | Differential sensitivity to surface compliance by tactile afferents in the human finger pad[END_REF][START_REF] Frey | Encoding touch and the orbitofrontal cortex[END_REF][START_REF] Esposito | Human Prefrontal Cortex Is Not Specific for Working Memory: A Functional MRI Study[END_REF] observed in Fig. 5 is considered as the best frequency for Meissner endings and as the peripheral stimuli reach the cortical level [START_REF] Mountcastle | Cortical neuronal mechanisms in fluttervibration studied in unanesthetized monkeys. Neuronal periodicity and frequency discrimination[END_REF].

The stimulation being different between the real and virtual velvet fabrics prompted the brain activity to encode the stimuli evoked by the virtual fabric as a novel texture (rather than to retrieve the velvet texture). In addition, the real and virtual velvets may have shown different compliance. Indeed, Condon et al. [START_REF] Condon | Differential sensitivity to surface compliance by tactile afferents in the human finger pad[END_REF] have reported different sensitivity to surface compliance by tactile afferents in the human finger pad. SAI (Merkel endings) and FAI (Meissner endings) afferents appeared to be well suited to carry compliance information whereas FAII (Pacini endings) played a minor role. The grounds for this suggestion are twofold. When the difference was maximal between the real and the virtual fabrics, the left orbitofrontal cortex was more active for the virtual novel texture than for tactile exploration of the familiar velvet fabric. Indeed, Frey et al. [START_REF] Frey | Encoding touch and the orbitofrontal cortex[END_REF] demonstrated a strong relationship between the orbitofrontal cortex and the attempt to encode tactile information which is consistent with the role of the orbitofrontal cortex for recognition memory. For instance, these authors showed a peak of increased activity in the orbitofrontal cortex when comparing (with positron emission tomography methods) the tactile exploration of novel stimuli from a related set of textures with familiar tactile stimuli in normal human subjects. The present findings in this study, together with results of Frey et al. [START_REF] Frey | Encoding touch and the orbitofrontal cortex[END_REF], demonstrate that the orbitofrontal cortex is involved in the active encoding of novel tactile information. Together with the orbitofrontal activity, in the virtual tactile encoding condition, there was a selective increase of activity of the dl-PFC within the left hemisphere and in the right hemisphere as well. The dl-PFC activity may witness the monitoring and manipulation of actively maintained information for retrieval of similar texture information when facing novelty in the stimuli. This is in line with literature that has also suggested the role of the dl-PFC activity during working memory tasks (WM), a system that is used for temporary storage and manipulation of information and that is involved in many higher cognitive functions [START_REF] Esposito | Human Prefrontal Cortex Is Not Specific for Working Memory: A Functional MRI Study[END_REF][START_REF] Owen | The Functional Organization of Working Memory Processes Within Human Lateral Frontal Cortex: The Contribution of Functional Neuroimaging[END_REF][START_REF] Smith | Storage and Executive Processes in the Frontal Lobes[END_REF].

For instance Braver et al. [START_REF] Braver | Direct Comparison of Prefrontal Cortex Regions Engaged by Working and Long-Term Memory Tasks[END_REF] reported bilateral dl-PFC region, i.e. BA 46/9, activation during working memory (WM) but not during either long-term memory (LTM) encoding or retrieval.

Besides, the increased activity of the left PPC when dealing with the virtual velvet new stimuli is in line with its critical role in specific processing of the perceived kinaesthetic cues during action-related somatosensory information processing [START_REF] Hartmann | Functional Connectivity in Tactile Object Discrimination-A Principal Component Analysis of an Event Related fMRI-Study[END_REF]. The frontoparietal network observed here for the virtual velvet fabric is in agreement with Cavada and Goldman-Rakic [START_REF] Cavada | Posterior parietal cortex in rhesus monkey: II. Evidence for segregated corticocortical networks linking sensory and limbic areas with the frontal lobe[END_REF] who showed in monkeys that all frontoparietal connections are reciprocal, and although they are most prominent within a hemisphere, notable interhemispheric connections are also present.

The present neuroimaging data point to the conclusion that tactile information from the virtual velvet fabric deviates significantly from expectations and therefore is considered as a novel fabric.

By contrast to the velvet fabric, the high congruence in frequency bands for the twill between real and virtual textures seems to favour perceptual categorisation and judgements. Indeed, for all the participants the sensory representation of the virtual fabric was close to the real one. The observed increased activity for the virtual twill fabric as compared to the real fabric in the left frontopolar PFC and anterior premotor cortex is in line with brain activation reported during perceptual judgement. The conversion of a sensory signal from the periphery and reaching the primary somatosensory cortex into perceptual categorisation as here with twill, was reported in the literature to involve premotor areas of the frontal lobe [START_REF] De Lafuente | Neural correlate of subjective sensory experience gradually builds up across cortical areas[END_REF]. For instance, these authors showed in monkeys that the activity arising from the somatosensory cortex during vibrotactile stimuli gradually relates more to the perceptual reports as it reaches the premotor areas. Indeed, they showed a correlation between neuronal responses of neurons within ventral, dorsal and medial premotor areas and perceptual judgements during detection tasks. Frontopolar activity also reported in the current study has been previously associated with retrieval from long-term memory [START_REF] Lepage | Prefrontal cortex and episodic memory retrieval mode[END_REF]. However, Braver et al. [START_REF] Braver | Direct Comparison of Prefrontal Cortex Regions Engaged by Working and Long-Term Memory Tasks[END_REF] failed to find frontopolar regions to be selectively engaged by retrieval. Nevertheless, the crucial role of the PFC during tactile memory processing is well established [48].

CONCLUSION

In this study the COF and the friction induced vibrations from the finger and different surfaces are studied. The surfaces investigated are real or virtual velvet and twill fabrics. The virtual fabrics are simulated with a tactile device. The velvet fabric presents a regular hairy surface, and the twill fabric has a grooved surface. The real and virtual fabrics are compared in terms of the finger response to friction, i.e. coefficient of friction and induced vibrations, and brain activation, by electroencephalography.

The brain activation comparing real and virtual fabrics concerned different areas for twill and for velvet fabrics. In fact, between real and virtual twill fabrics the brain activation presents similarities but for the velvet texture there are important differences. The results show the rendering of virtual fabrics is good in terms of COF. This confirms the fact, well known in the literature, that the COF is not sufficient to describe the tactile rendering of textile fabrics. A deeper analysis in terms of finger induced vibrations shows some similarities and differences between real and virtual surfaces which can explain the difference of rendering between real and virtual textures for velvet and twill fabrics. In fact, the rendering before 100 or 200 Hz is satisfactory for twill and far less for velvet fabric. Up to these frequencies the fabric simulations have to be improved for both fabrics. Therefore, it can be concluded that the difference in vibrotactile stimulation in a specific bandwidth, in the range of sensitivity of both Meissner and Pacinian endings, prompts the brain to change the cortical areas that are activated. For the virtual velvet, areas are required in encoding of a novel texture, and for the virtual twill, areas are involved in the retrieval of perceptual categorisation.

[48] Romo R, Salinas E. Flutter Discrimination: neural codes, perception, memory and decision making. Nature Reviews Neuroscience. 2003;4:203.

List of figures:

  with f: the frequency in Hz, Δf: the considered frequency bandwidth, RMS(f): the root mean square of the acceleration at the f frequency in m/s², C: factor depending on the weighing window used, in this case it is a Hanning window and C=1.5.

  active and Driven Right Leg passive electrodes. The signals were pre-amplified at the electrode sites and post-amplified with DC amplifiers, filtered on-line with a 0.16 Hz high pass filter (Actiview acquisition program) and digitised at a sampling rate of 1024 Hz and resampled at 1000 Hz offline.

Figure 1 :

 1 Figure 1: Investigated surfaces a) 2/1 twill, b) twill with a dashed line on one rib (the arrow

Figure 2 :

 2 Figure 2: a) Participant during an experiment and b) an index finger equipped with the

Figure 3 :

 3 Figure 3: Tangential force (N) during the back and forth lateral movement of 40 mm in each

Figure 4 :

 4 Figure 4: Procedure to obtain the coefficient of friction (case of the real twill for one subject):

Figure 5 :

 5 Figure 5: Typical acceleration autospectra obtained from a) the real and b) the virtual velvet

Figure 6 :

 6 Figure 6: Typical acceleration autospectra obtained from the twill fabric a) and b) with the real

Figure 7 :

 7 Figure 7: Coefficients of friction of real and virtual velvet fabrics. A dot corresponds to a

Figure 8 :

 8 Figure 8: Power of the acceleration from a) 3 to 1000 Hz, b) 3 to 100 Hz and c) 100 to 400 Hz

Figure 9 :

 9 Figure 9: Power from 100 to 400 Hz relative to power from 3 to 100 Hz for both real and virtual

Figure 10 :

 10 Figure 10: Statistical source estimation maps for real vs virtual velvet fabrics contrast.

Figure 11 :

 11 Figure 11: Mean coefficient of friction of real and virtual twill fabrics. A dot corresponds to a

Figure 12 :

 12 Figure 12: Power of the acceleration from a) 3 to 1000 Hz, b) 3 to 200 Hz and c) 200 to 400 Hz

Figure 13 :

 13 Figure 13: Power from 200 to 400 Hz relative to power from 3 to 200 Hz for both real and

Figure 14 :

 14 Figure 14: Statistical source estimation maps for real vs virtual twill fabrics contrast. Significant

Table 1 :

 1 Synthesis of the obtained results in terms of COF, finger induced vibrations and brain activation.

  Figure 1

  Figure 2

Figure 3 Figure 4

 34 Figure 3

Acknowledgements

The authors thank the CNRS for the financial support of the DISREMO project. The authors are deeply grateful to all the participants from the University of Haute Alsace who participated and gave their time freely.

Ethical statements

The authors declare that they have no conflict of interest.

All procedures performed in studies involving human participants were carried out in accordance with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent was obtained from all individual participants included in the study.