Keywords: Bioimpedance, biological cells, biomedical electronics, biosensors, cellular biophysics, impedance measurement, physiology

The impedance of one cubic centimeter of living tissues of potato and guinea pig were measured from 500 Hz to 3 MHz. In general, the magnitude of the impedance was found to monotonically decrease with increasing frequency. This implies that the membrane of each cell in the tissue acts like a capacitor, which is in parallel with a membrane resistance. The membrane resistance and capacitance together are in series with a protoplasm resistance. Experimentally, it was observed that after the guinea pig died, the membrane resistance of its muscle decreased from 1.49 kΩ to 0.79 kΩ while the protoplasm resistance remained around 0.11 kΩ . By contrast, when the potato started to germinate, the protoplasm resistance decreased from 0.25 kΩ to 0.10 kΩ , while its membrane resistance remained around 4 kΩ .

I. INTRODUCTION

N A PREVIOUS publication [START_REF] Philippson | Sur la resistance electrique des cellules et des tissus[END_REF], we have outlined a method for producing alternating currents between DC and 3 MHz, and for measuring at these frequencies the electrical resistance of living tissues of plants or animals. These studies established the general principle of the electrical resistance of living tissues as a function of the frequency and certain tissue parameters.

The present experimental results (Figs. [START_REF] Philippson | Sur la resistance electrique des cellules et des tissus[END_REF] to 3) show that, in general, the electrical resistance of tissues, measured in ohm/cm 3 , decreases monotonically from DC to infinite frequency. Therefore, the tissue resistance must be shunted by a capacitance C, so that its impedance decreases with the frequency f as 1 2πfC .

II. THEORY

We can experimentally demonstrate the existence of a capacitance in a living tissue. For example, let us take a cylinder of tissue from a potato with a measured resistance of 640 ohms at 100 kHz. Let us then take an inductive coil of about 10 5 turns and 6 cm in diameter with a resistance of about 400 ohms at 100 kHz. Connecting the coil in series with the tissue cylinder, their total resistance becomes 380 ohms. This is because the magnitude of the impedance Z of a resistance R in series with an inductance L and a capacitance C is ( ) ( ) is the angular frequency. (The impedance of any network, however complicated, can be similarly simplified.) This shows that, when the addition of an inductance decreases the resistance of a network, the network must include a capacitance.

Based on the above observations, we hypothesize that the physiological membrane bounding a cell in the tissue can act as a capacitor. On the one hand, the membrane, essentially formed by lipids, resembles a perfect dielectric. On the other hand, the membrane is normally impermeable, not very permeable, or semi-permeable to electrolytes. (It is essential to distinguish the physiological membrane from the histological membrane. The former confines the cellular content and governs the physical process of absorption and the physiological process of permeability. The latter includes cellular secretion, which is part of the intercellular space. The thickness of the physiological membrane is on the order of a molecule.)

The cellular content and intercellular space on either side of the membrane conduct electric current and form the electrodes of the capacitor with the membrane as the dielectric. However, the electrical resistance is quite high for both the intracellular and intercellular media, since their main carrier of the electric current is a low-concentration solution of salt ions. This resistance is in series with the membrane capacitance.

In addition to the membrane capacitance, the membrane has a finite electrical resistance. If we consider a membrane across the entire tissue cylinder and perpendicular to the direction of the electric current, we find the membrane dielectric is interposed between the intercellular spaces. Therefore, based on what we just discussed, we must consider the membrane capacitance is shunted by a resistance.

It follows that the tissue can be represented electrically by a resistance R in series with a capacitance C, with C shunted by another resistance r. R is the intrinsic electrolytic resistance of the cell protoplasm and the intercellular spaces of the tissue cylinder; C and r are the capacitance and resistance of the cell membranes in the tissue cylinder. The impedance Z of such a network is given by ( )

2 2 2 2 2 2 1 ω ω + = + + Rr r Z R r C . ( 1
)
At DC, ( )

0 = + Z R r , (2)
University, Ithaca, NY 148523, USA (e-mail: jch263@cornell.edu). O. P.-R. is with LAAS-CNRS, Toulouse University, 31400 Toulouse, France.

Principles of the Electrical Resistance of Living Tissue

Maurice Philippson I which sets the upper limit of Z.

At the infinite frequency, ( )

∞ = Z R,
(3) which sets the lower limit of Z. From (2) and (3), ( ) ( )

0 r Z Z = - ∞ . ( 4
)
Knowing the approximate values of R and r, we can use (1) to calculate C at each frequency, ( )

2 2 2 2 1 ω ω + - - = Rr r Z R C r . (5)
Based on this calculation, we see that C is not constant and its value decreases with frequency (Tables I to III). This should not surprise us. The capacitance of a capacitor is determined by its dimensions and the permittivity of the dielectric between the electrodes, and we know [START_REF] Chwolson | Traité de Physique[END_REF] that the permittivity of nongaseous dielectrics decreases with frequency.

To study this phenomenon in the tissues, we plot in Figs. 1 to 3 the frequency dependence of the capacitance calculated by (5) from the measured impedance magnitude. With the capacitance and frequency both plotted on a logarithmic scale, it can be seen that the frequency dependence is indeed linear. Note that in these figures, circular symbols indicate measured impedance magnitudes and calculated capacitances by (5); solid curves indicate impedances calculated by (8) and capacitances calculated by (7). All measurements are performed at 25.5 °C on a cubic centimeter of tissue.

Apparently, the capacitance satisfies the following equation over a wide bandwidth:

( ) ( ) ' log log ' log ω ω ω α ω = + C C . ( 6
)
The slope of the frequency dependence α can be determined graphically.

From (6), we have

( ) ( ) ' ' constant α α ω ω ω ω ⋅ = ⋅ = C C
.

Let the constant be C 1 , the capacitance at any frequency is given by ( )

1 α ω ω - = ⋅ C C . ( 7
)
Substituting ( 7) in (1), we have ( ) Having experimentally validated our hypotheses, we can start to analyze the phenomenon we are studying. Indeed, in (7) if ω approaches zero (close to DC), C approaches infinity. This means that the permittivity of the dielectric membrane approaches infinity. This implies the impedance of the membrane capacitance is a polarization reactance, which seems consistent with ongoing experiments on the impedance of copper-ferrocyanide membranes. In this case, the polarization reactance of a semipermeable membrane is ( )

( ) 2 2 2 1 2 2 1 2 1 α ω ω - + = + + Rr r Z R r C . ( 8
1 1 1 α ω - = P X j C . ( 9
)
The symbol j denotes the square root of -1 and indicates X P is in phase with the current flowing through the capacitor. Let

1 1 β = C , then ( ) 1 α β ω - = P X j . ( 10
)
The parameter β in 3 Ω cm is the polarization reactance at the unity frequency. Substituting (10) into (8) gives ( )

( ) 2 2 2 1 2 2 2 1 α ω ω β - + = + + Rr r Z R r . (11)
In (11), R in 3 Ω cm is the electrical resistance of the protoplasm and the intercellular spaces of the tissue under study. Expressed in resistivity, it is the inverse of conductivity. It indicates the state of electrolytes in the protoplasm. The parameter r in 3 Ω cm is the ohmic resistance of the cell The question now is whether or not these parameters are fixed for a given tissue in a given physiological state, but variable with physiological changes.

III. EXPERIMENT

The three series of measurements that we carried out on the liver of a guinea pig immediately after it is killed and bled agreed very well (Table I and Fig. 1). This demonstrates the stability of the tissue parameters and the precision of the measurement technique. By contrast, when we measured the muscle of the same animal, we found the tissue parameters changed rapidly resulting in mismatched data. To study these changes, we compare a series of measurements taken immediately after bleeding the animal (characteristic of the fresh tissue) with a second series of measurements made about an hour after the animal died (Table II and Fig. 2). The comparison shows that upon death the membrane impedance decreases noticeably, while the protoplasm resistance R remains constant. Additionally, the frequency dependence of the tissue capacitance is the same for a cooler and denser tissue, indicating the parameter α remains constant while the membrane capacitance C 1 increases. This implies that the polarization reactance β decreases along with the membrane resistance r.

Finally, we made two series of measurements on potatoes, in March during the winter dormancy and in April at the start of germination. This time, the results (Table III and Fig. 3) show a very large decrease in protoplasm resistance R, indicating the mobilization of the salt reserve, without changing membrane parameters such as r, C1, α , and β . In fact, the same straight line satisfies the calculated logarithmic capacitances for the two series of measurements. Therefore, we can use these parameters to analyze cell physiology, in particular, the link between the changes in these parameters and variations in the permeability of cell membranes.

IV. CONCLUSION

The study of the electrical resistance of living tissues between 500 Hz and 3 MHz gave us the following:

1) In general, a cell membrane conducts alternating current like a capacitor.

2) The electrical conductivity of a living tissue can be expressed by the two following equations, which differ from each other only by the definition of the parameter C1:

- - - - 101 - - ∞ - 250 - - - 100 - - ( ) ( ) 2 2 2 1 2 2 1 2 1 α ω ω - + = + + Rr r Z R r C . (8) ( ) ( ) 2 2 2 1 2 2 2 1 α ω ω β - + = + + Rr r Z R r . ( 11
)
3) The polarization reactance of a cell membrane is analogous to that of a capacitor and is expressed by

( ) 1 α β ω - = P X j . ( 10
)
In the above equations the symbols are defined as in the following:

Z in 3 Ω cm is the impedance of a cubic centimeter of tissue at the frequency f in Hz.

X P in 3 Ω cm is the specific polarization reactance at the frequency f. j is an operator indicating that the current is shifted by a quarter period ahead of the voltage. R in 3 Ω cm is the specific resistance of the protoplasm and intercellular spaces in the tissue. r in 3 Ω cm is the ohmic resistance of the membranes in the tissue cube.

C 1 in F/cm 3 is the membrane capacitance in the tissue cube at the unity frequency.

β in 3 Ω cm is the polarization reactance of the cell membranes in the tissue cube at the unity frequency. The last two parameters have an inverse relationship as in

1 1 β = C .
α is a numerical coefficient indicating the rate of decrease in the polarization reactance of the capacitor as a function of the frequency according to (7).

4) The parameter R characterizes the physio-chemical state of protoplasm. The parameters r, C 1 , α , and β characterize the physiological state of the membranes. 5) With changes in the physiological state of the tissue, these parameters can vary independently.

  by James C. M. Hwang and Olivia Peytral-Rieu. J. C. M. Hwang is with the Department of Materials Science and Engineering, Cornellwhere 2πf ω =

Fig. 1 .Frequency

 1 Fig. 1. Impedance of bled guinea pig liver. Frequency (Hz) 10 2 10 3 10 4 10 5 10 6 10 7

  ) Using (8), calculated values of |Z| are listed in Tables I to III and plotted in Figs. 1 to 3. It can be seen that the calculated values are very close to the measured data.

Frequency

  , α = 0.41 1 h after Bleeding, α = 0.41 R = 0.11 kΩ r = 1.49 kΩ C 1 = 0.42 μF β = 0.38 MΩ R = 0.11 kΩ r = 0.79 kΩ C 1 = 0.61 μF β = 0.26 MΩ Impedance Magnitude (Ω) Capacitance (F) Impedance Magnitude (Ω) Capacitance (F) Measured Calculated Calc. by (5) Calc. by (7) Measured Calculated Calc. by (5) Calc. by (7) 500 1,580

Fig. 2 .Frequencyparameter β in 3 Ω

 23 Fig. 2. Impedance of bled guinea pig muscle. Frequency (Hz) 10 2 10 3 10 4 10 5 10 6 10 7

Fig. 3 .Frequency

 3 Fig. 3. Impedance of potato. Frequency (Hz) 10 2 10 3 10 4 10 5 10 6 10 7

TABLE I IMPEDANCE

 I OF BLED GUINEA PIG LIVER R = 0.20 kΩ, r = 1. 78 kΩ, C 1 = 0.59 μF, α = 0.49, β = 0.2.7 MΩ

	Frequency (Hz)	4 W	Impedance Magnitude (Ω) Measured 12 W 18 W Average	Calculated	Capacitance (F) Calculated Calculated by (5) by (7)
	500	1,950	1,700	2,200	1,950	1,957	3.2 × 10 -8 2.96 × 10 -8
	1,000	1,900	1,715	2,250	1,948	1,934	1.63 × 10 -8 1.96 × 10 -8
	2,000	1,900	1,695	2,180	1,925	1,913	1.1 × 10 -8 1.44 × 10 -8
	5,000	1,700	1,625	1,965	1,763	1,775	9.25 × 10 -9 9.06 × 10 -9
	10,000	1,625	1,510	1,800	1,645	1,610	5.75 × 10 -9 6.46 × 10 -9
	20,000	1,490	1,345	1,585	1,475	1,390	3.8 × 10 -9 4.6 × 10 -9
	50,000	1,070	875	1,025	990	1,036	3.15 × 10 -9 2.90 × 10 -9
	100,000	800	680	855	780	800	2.17 × 10 -9 2.09 × 10 -9
	200,000	615	525	639	595	598	1.5 × 10 -9 1.5 × 10 -9
	500,000	440	382	447	425	417	9.25 × 10 -10 9.5 × 10 -10
	1,000,000	327	296	351	325	326	6.9 × 10 -10 6.8 × 10 -10
	1,250,000	300	285	325	303	300	-	-
	1,500,000	280	274	300	285	290	-	-
	2,000,000	270	260	294	275	270	4.4 × 10 -10 4.8 × 10 -10
	2,500,000	248	249	272	255	255	-	-
	3,000,000	235	-	255	245	242.5	4.16 × 10 -10 3.9 × 10 -10
	10,000,000	-	-	-	-	215	-	-
	∞	-	-	-	-	200	-	-


Zakarya Soufi
email: zakarya.soufi@grenoble-inp.fr

Pierre David

Zakaria Yahouni

A Reference Data Model for Material Flow Analysis in the context of Material Handling System Design and Reconfiguration

Keywords: Manufacturing Systems, Material Handling Systems, Material Flow Analysis, Reference Data Model

The design and reconfiguration of Material Handling Systems (MHS) at the factory scale is known to be complex. Various data and analyses are required to define the internal logistics needs the MHS must fulfill. In the literature, the identification of the MHS' needs is performed through Material Flow Analysis (MFA). The MFA is expressed through charts and diagrams which are manually developed. The manual development of charts and diagrams leads to gathering data in a disseminated way. Additionally, MFA is differently addressed in the literature; each work analyzes a different and restrained set of data. In this paper, we aim to generalize MFA by proposing a Reference Data Model (RDM) using UML (Unified Modeling Language) class diagrams. It allows listing and structuring all the data required for the MFA. The RDM can be used to conduct a data-driven MFA which enables data integrity and the reduction of the development time of charts and diagrams. A proof of concept is also given to show the ability to simultaneously generate charts and diagrams, while ensuring data integrity.

INTRODUCTION

Material Handling Systems (MHS) address storing, packaging, and moving products. It plays a key role in the performance of the entire manufacturing system [START_REF] Esmaeilian | The evolution and future of manufacturing: A review[END_REF]. An efficiently designed MHS leads to effective production management, improvement of on-time delivery, and enhancement of production quality [START_REF] Montoya-Torres | A literature survey on the design approaches and operational issues of automated wafer-transport systems for wafer fabs[END_REF]. The design of modern manufacturing systems can be very complex and the resulting system can be a source of excessive expenditure if it is not efficiently designed [START_REF] Bouh | Material handling equipment selection: New classifications of equipments and attributes[END_REF]. In such design processes, many dimensions should be integrated as the dynamic behavior of the system, information systems, materials, the interaction between operators and machines, etc. In this work, MHS is seen as the interaction between Material Handling Equipment (MHE) and operators within the manufacturing system. All the elements constituting the MHS must function as a whole to meet the required system objectives [START_REF] Noble | A framework for material handling system design justification[END_REF]. Before proceeding to the design and reconfiguration of such systems, a tremendous amount of data is needed to take the appropriate design decisions (e.g. deciding the level of automation of Material Handling Activities, selecting the set of MHE, etc.) [START_REF] Noble | A framework for material handling system design justification[END_REF]- [START_REF] Shell | Material Handling and Storage Systems[END_REF]. As in any systems engineering process, the efficiency of the MHS design process depends on the correct identification and understanding of the needs and requirements. For MHS design, the needs analysis is usually done through the Material Flow Analysis (MFA). In the literature, MFA is considered to be the first step of the MHS design and reconfiguration [START_REF] Stephens | Material Handling[END_REF]. It is defined as the systematic assessment of flows and stocks of materials within a system defined in space and time. In the literature, MFA is addressed in various ways in terms of the targeted data. For instance, in [START_REF] Starbek | Optimization of material flow in production[END_REF] the authors focus on the analysis of the paths that are taken by different family parts to perform the MFA. While in [START_REF] Longo | Material flow analysis and plant layout optimization of a manufacturing system[END_REF] other aspects are analyzed, such as the product's characteristics and dimensions. However, it can be seen that in the literature the MFA is not unified, but the different addressed concepts should be related to one another. Additionally, the existing MFA techniques mainly consist of manually executed procedures such as building charts and diagrams [START_REF] Stephens | Manufacturing Facilities Design & Material Handling[END_REF] (E.g. From-To charts, Material flow diagrams, Spaghetti diagrams, etc.). These manual approaches can suffer from several drawbacks, especially in a large-scale manufacturing system; different MFA charts and diagrams have to be developed separately to describe the MHS' needs without digitization nor ensuring data integrity. Thus, a proposition may be formulated to unify and generalize the MFA practices to make them compatible and complete. A basis to generalize MFA would be to propose a Reference Data Model (RDM) to clarify what data should be considered in an MFA and how they are articulated. Moreover, the proposal of an RDM opens the path to a datadriven MFA. Data-driven approaches allow providing services for MFA such as charts and diagrams generation while reducing the development time and ensuring data integrity. In the work of [START_REF] Meng | Data-driven modeling and simulation framework for material handling systems in coal mines[END_REF], the authors proposed a data-driven approach to collect data related to the MHS of coal mines and to generate simulation models. This work shows the benefits of a datadriven approach such as; the automatic generation of simulation models, the reduction of model development cost and time, and the replicability of the analysis approach to similar systems. The main drawback of the RDM proposed in [START_REF] Meng | Data-driven modeling and simulation framework for material handling systems in coal mines[END_REF] is that it is specialized for a limited type of MHS (coal mines MHS). The contribution of this paper is to propose an RDM to generalize and unify the data manipulated in MFA. To propose a relevant RDM, data are identified and selected from the current practices of MFA reported in the literature. The RDM is represented in UML (Unified Modeling Language) class diagrams. The ability to exploit the RDM in a data-driven MFA process is demonstrated with proof of concept examples of MFA views generation. The remaining of this paper is organized as follows; It starts with a literature review on Material Flow Analysis and Datadriven approaches. Afterward, in the 3rd section, an RDM for MFA is proposed and an application example is given. Finally, the conclusions and perspectives are given in the last sections.

STATE OF THE ART

Material Flow Analysis

In the industrial area, the literature shows that articles use the MFA to examine the movement of the material over time [START_REF] Shell | Material Handling and Storage Systems[END_REF].

It can be used to analyze the whole supply chain [START_REF] Starbek | Optimization of material flow in production[END_REF][START_REF] Cencic | Material Flow Analysis with Software STAN[END_REF], or it can focus on the analysis of MHS [START_REF] Shell | Material Handling and Storage Systems[END_REF][START_REF] Lockamy | Examining supply chain networks using V-A-T material flow analysis[END_REF][START_REF] Wohlgemuth | Combining discrete event simulation and material flow analysis in a component-based approach to industrial environmental protection[END_REF]. The steps of MFA may vary depending on the objective of the analysis. For example, it can be used for; optimization purposes [START_REF] Starbek | Optimization of material flow in production[END_REF], waste management [START_REF] Cencic | Material Flow Analysis with Software STAN[END_REF], simplification of the material flows in the facility [START_REF] Shell | Material Handling and Storage Systems[END_REF], or for the plant layout design [START_REF] Longo | Material flow analysis and plant layout optimization of a manufacturing system[END_REF]. However, data collection remains a common step. In the context of MHS design, MFA is mainly conducted through manual procedures such as charts and diagrams. These graphical representations help to gather relevant data for MHS design, for example;  Production sheet [START_REF] Longo | Material flow analysis and plant layout optimization of a manufacturing system[END_REF]: it allows the collection of data relatively to each phase of the manufacturing process.  Working sheet [START_REF] Longo | Material flow analysis and plant layout optimization of a manufacturing system[END_REF]: it gives the possibility to compare foreseen values (production time and quantity) with real values.  Flow chart [START_REF] Stephens | Manufacturing Facilities Design & Material Handling[END_REF]: it allows to study of the material flow of each product family (see figure 3).  Process flow layout [START_REF] Stephens | Manufacturing Facilities Design & Material Handling[END_REF]: It allows to identify the existing flow path on a layout for the products made by the company (see figure 5).  From-to chart [START_REF] Stephens | Manufacturing Facilities Design & Material Handling[END_REF]: it displays the flow of material between functional areas of a plant based on a specific handling unit (see figure 4). The articles addressing the MFA, in the context of MHS design and reconfiguration, usually focus on a restrained set of data. For example, in [START_REF] Cencic | Material Flow Analysis with Software STAN[END_REF][START_REF] Wohlgemuth | Combining discrete event simulation and material flow analysis in a component-based approach to industrial environmental protection[END_REF] the authors only use flow charts to perform the MFA. While in [START_REF] Stephens | Manufacturing Facilities Design & Material Handling[END_REF] the authors focus on other charts and diagrams, such as string diagrams and fromto charts These manual procedures are time-consuming and difficult to exploit; Having different charts and diagrams that are separately developed without data centralization does not ensure data integrity. In the literature, RDMs are used to adapt data-driven approaches. It allows better exploitation of data by giving the possibility to centralize data, thus, ensuring data integrity. An opportunity is to provide an RDM covering the various MFA practices and allowing a robust data utilization.

Data-driven approaches

With the latest information and computing technology innovations, new opportunities can be identified for MFA, such as data-driven approaches. It helps to develop models to describe systems with similar features and functionalities [START_REF] Stephens | Manufacturing Facilities Design & Material Handling[END_REF][START_REF] Meng | Data-driven modeling and simulation framework for material handling systems in coal mines[END_REF][START_REF] Cencic | Material Flow Analysis with Software STAN[END_REF][START_REF] Lockamy | Examining supply chain networks using V-A-T material flow analysis[END_REF][START_REF] Wohlgemuth | Combining discrete event simulation and material flow analysis in a component-based approach to industrial environmental protection[END_REF][START_REF] Abdellaoui | Scalable, reconfigurable simulation models in industry 4.0oriented enterprise modeling[END_REF]. It can be adapted to support the design and operational decision-making in MHS [START_REF] Mcginnis | The Future of Modeling in Material Handling Systems[END_REF]. The most popular language for such approaches is UML (Unified Modeling Language). It is mostly used for describing a data-capturing operation [START_REF] Mcginnis | The Future of Modeling in Material Handling Systems[END_REF]. In [START_REF] Meng | Data-driven modeling and simulation framework for material handling systems in coal mines[END_REF], the authors propose data-driven modeling and simulation based on an RDM. However, the proposed RDM can not be considered a generic model for MFA in the context of MHS; It focuses on the simulation of the equipment and the processes in coal mines. The information model in this work describes the data requirements for the construction and execution of a simulation model; Necessary data is retrieved following a specific data format. To reach the final result of this work, system specifications in coal mines had to be listed; MHS components, processes, and flows are represented in flow charts. Later on, UML classes are progressively constructed to represent the different aspects that were shown in the flow chart. Such approaches give the possibility to realize model transformation while ensuring data integrity. The model transformation enhances the benefits of proposing an RDM for the generalization of MFA; It allows to describe and understand the system by generating different charts and diagrams simultaneously while ensuring data integrity. This proposition would reduce the costs, time, and errors that are derived from the manual procedures that are used in the literature. In this article, we aim to propose an RDM to conduct the MFA in the context of MHS; This generic model would allow users to describe the MHS needs of different industrial cases. Further descriptions are presented in the following section.

REFERENCE DATA MODEL FOR MATERIAL FLOW ANALYSIS

In the following sub-sections, before proposing our model, the literature is analyzed to derive a list of parameters that must be represented in the RDM. The goal is to define a wide range generic data structure encompassing the previous works on MFA

Data definition

The development of an RDM requires a consolidated list of parameters. In our case, parameters are needed to describe the different parts and interactions that can be found in MFA in the context of MHS design and reconfiguration. These elements allow the creation of an MFA meta-model that will support the analysis. The literature is analyzed to propose an RDM covering the existing practices of MFA. Articles were selected based on the journal's ranking, the number of citations, and compliance with the topic (MFA in the context of MHS design and reconfiguration).

MFA in the context of MHS is not a common subject in the literature, despite its importance to express the MHS' needs. Thus, the data identification is not only made on papers that address the MFA only but also on papers that discuss MHS issues in general. As a result, twenty-two articles were selected and only twelve are retained due to the redundancy in the mentioned data [START_REF] Montoya-Torres | A literature survey on the design approaches and operational issues of automated wafer-transport systems for wafer fabs[END_REF][START_REF] Shell | Material Handling and Storage Systems[END_REF][START_REF] Ioannou | An integrated model and a decomposition-based approach for concurrent layout and material handling system design[END_REF][START_REF] Klausnitzer | Optimal facility layout and material handling network design[END_REF][START_REF] Longo | Material flow analysis and plant layout optimization of a manufacturing system[END_REF][START_REF] Stephens | Manufacturing Facilities Design & Material Handling[END_REF][START_REF] Wohlgemuth | Combining discrete event simulation and material flow analysis in a component-based approach to industrial environmental protection[END_REF][START_REF] Mcginnis | The Future of Modeling in Material Handling Systems[END_REF][START_REF] Sgarbossa | Cloud material handling systems: Conceptual model and cloud-based scheduling of handling activities[END_REF][START_REF] Vieira | Using simio to automatically create 3d warehouses and compare different storage strategies[END_REF][START_REF] Ezema | Industrial design and simulation of a JIT material handling system[END_REF][START_REF] Granlund | Designing internal logistics systems fit for the future[END_REF]. The analysis led to the identification of 197 parameters grouped into 42 categories (such as machine data, product data, flow data, etc.). Afterward, a correlation analysis was conducted to reduce the list of parameters by keeping the generic ones and removing the parameters addressing the same concept (for example; aisle, corridor, and alley can be combined in the concept of route). As a result, a list of 59 parameters is selected and grouped into three main data categories; Product features, Material Handling System, and Manufacturing System.

Data structuring using class diagram

Once the data labels (parameters) are identified, UML classes are used to provide a view of the RDM for MFA. The toplevel data is presented in figure 2a. This MFA class is a composition of three main classes represented in different packages:

 Product (figure 2b  MHS (figure 2d): this package describes two main aspects; The layout of the shop-floor (through Route Network and Route classes). And the characteristics of the MHS. The MHS class is composed of the three categories of MHE (moving equipment, packaging equipment, and storage equipment). The separation of these categories allows a better description of each class, for example, it can be seen that the moving equipment requires more parameters than the other MHE categories. Moreover, the performance of MHS can be expressed through the Flow class.

This RDM summarizes the different data that are needed to generalize the data that may be part of MFA. Besides, the RDM can be exploited using a data-driven approach to facilitate the MFA. The following section shows a demonstrator of a data-driven MFA used in a real case study.

Application example

To demonstrate the use of our proposal, a real case study was conducted to perform the data-driven MFA. The case concerns a plant of safety equipment manufacturer (climbing gear, caving gear and work-at-heigh equipment). The shop-floor is composed of 21 production machines arranged in five production cells.

To proceed to the data-driven MFA, the RDM was first implemented on an online database management system. Then, the users filled the data needed for the MFA in the database. Afterward, the data was extracted using a software program that we developed. Finally, different MFA charts and diagrams were simultaneously generated while ensuring data integrity, some examples can be seen in figures 3, 4, and 5.  The flow chart (see figure 3) was generated to identify the path of the three product types.  The from-to chart (see figure 4) was used to display the number of containers moved between the five production cells per week.  The process flow (see figure 5 A proof of concept for data-driven MFA is given in a case study To propose a consistent RDM, 197 parameters were identified from 12 articles. Later on, 57 parameters were selected using correlation analysis to remove the redundancies and keep the relevant parameters. As a result, four data packages are selected to structure the data; Top data package, Manufacturing System package, MHS package, and Product package.

For future development, an MFA toolset can be created to generate automatically other MFA charts and diagrams based on the collected set of data. The automatic generation of such models would help to adapt to the new visualization needs in a short amount of time and with fewer costs. Furthermore, the proposed RDM is also exploited in another work to propose a generic, scalable, extensible, and data-driven simulation model. In this work, the automatic generation of the simulation allows the analysis of the performance of the MHS and the design alternatives. The obtained results are the subject of a submission to a journal.

  ): This package is composed of three classes; Product class, Family class, and Handling Unit class. the parameters of this class help to describe the features of a given product. Each product belongs to a specific product family and might be handled in a specific container. That is why the Product class is linked to two other classes; Handling Unit, and Family.  Manufacturing System (figure 2c): this data category focuses on components of the manufacturing system; It starts with the description of the cell class, and just like the real manufacturing systems, the cell class is a composition of two other classes; Machine and Queue.

Figure 2a .

 2a Figure 2a. Top data level

  ) layout was used to represent the layout of the shop-floor. five The-shop floor is composed of 21 production machines arranged in five production cells. The shop-floor produces three The user starts first by filing the database following the RDM that we proposed in figures 2a, 2b, 2c, and 2d. The 4. DISCUSSION AND CONCLUSION Before the design or reconfiguration of the MHS, it is important to define the MHS' needs to take the appropriate decisions. In the literature, the MHS' needs are expressed by performing the MFA. The MFA is considered to be the beginning of any MHS design and reconfiguration processes. Yet, the conduction of the MFA is performed with a restrained set of data and is mainly done through error-prone and timeconsuming manual procedures. This opens up a new opportunity to propose an RDM to express the data needed for the MFA in the context of the MHS design and reconfiguration. The goal of this paper is to propose an RDM to generalize the MFA in the context of MHS. The RDM regroups different parameters that allow a precise description of MHS and an effective MFA; The proposed data structure gives the ability to adopt a data-driven MFA that can generate simultaneously different MFA charts and diagrams while reducing the

Figure 2d .Figure 3 .

 2d3 Figure 2d. Material Handling System package

Figure 4 .

 4 Figure 4. From/To chart of the handled containers/week between the 5 production cells

ACKNOWLEDGMENTS

The authors thank the French National Research Agency (ANR) that funded this research under the LADTOP project (grant ANR-19-CE10-0010-01).


H Brahimi
email: hbrahimi@laas.fr

H L Martinez-Reyes

P H Merrer

A Bouchier

O Llopis
email: llopis@laas.fr

A CAD APPROACH OF MICROWAVE OPTICAL SYSTEMS INCLUDING NOISE PERFORMANCE

A technique for the simulation of a microwave optical system is described. This technique, based on microwave CAD software, allows the simulation of the gain and noise performance. The optical devices are described using either an equivalent circuit approach or equation based models. The simulations of a simple RF optical link and of a more complex system, a microwave optical delay line frequency discriminator, are presented.

I. INTRODUCTION

Optical devices are more and more used in microwave systems, taking benefit of the low losses of the optical fibers, of their small size and their immunity to electrical parasitic signals. An example of these systems is the microwave optical oscillator, either based on optical resonators or delay lines, which can deliver ultra high spectral purity signals [START_REF] Yao | Progress in the optoelectronic oscillator -a ten year anniversary review[END_REF].

However, the performance of these systems is dependent on the performance of the devices used for the electrical to optical or optical to electrical conversions, on the chosen optical modulation technique, on the necessary microwave amplifiers, on the devices biasing circuits, on the quality of the optical fiber and, above all, on the topology chosen to build the whole system. It is thus important to be able to compute the system phase noise using an appropriate modelling approach. This analysis will allow us to understand where are located the main noise sources in the system, and how to improve the system performances by reducing these noise sources or their impact on the phase noise. Specific microwave circuit design softwares have been designed in the 90s in order to take into account the frequency conversion phenomena between noise sidebands around the different harmonics of the RF signal (including DC) [START_REF] Rizzoli | General noise analysis of nonlinear microwave circuits by the piecewise harmonic-balance technique[END_REF]. These softwares may be used to simulate the microwave parts of a microwave optical system. However, they generally do not include any specific model for the optical devices involved in these systems. A solution to this problem is in finding a representation of these devices which can be implemented in the microwave simulator, using either an equivalent electrical circuit or a mathematical model.

II. STUDY OF AN MZ BASED OPTICAL LINK: RF GAIN

The approach described in the part I has been implemented on a commercially available microwave simulation software: Agilent ADS.

In a first step, we began simulating a Mach Zehnder (MZ) based optical link. In the MZ modulator, the nonlinearity due to the 1+cos(x) optical response (x being the DC bias) leads to a saturation phenomenon which depends on the parameters of this curve: maximum optical power and maximum power voltage V 0 and extinction voltage V π (see Figure 1). These parameters are the input parameters of our MZ CAD model, as well as its frequency response which is modelled using a low pass filter on the modulator RF input port.

In our MZ based systems, we use two different types of modulation: the classical linear modulation (LM) and the optical carrier suppression (double sideband carrier suppression, or DSB-CS), which results in a frequency doubling of the RF signal. The last modulation type requires a high level of RF input power, but is more efficient in terms of signal to noise ratio if such an RF power is available [START_REF] Onillon | Optical links for ultra-low phase noise microwave oscillators measurement[END_REF], [START_REF] Onillon | Opticalmicrowave links for LO distribution in space systems[END_REF]. In the classical linear modulation, the MZ modulator is biased at (V 0 +V π  /)2, while in the optical carrier rejection mode, it is biased at V π . The optical source is described using a conventional RF source model of ADS (with a frequency of 200 THz !), and each optical element is described using ideal RF elements, such as ideal transmission lines.

Concerning the MZ modulator, it is described using an equivalent black box nonlinear equation SDD (Symbolically Defined Device). This SDD receives the optical signal from the laser on one input port, and the RF signal and the DC bias on the other input port. It performs the computation of the main system equation (1) which describes this device.

)) ) (

) ( ) ( cos( 1 ( 2 . 0 f V t V V V V L P P RF RF DC DC ins las opt π π π π η + - + =
(1) P opt being the optical power received by the photodiode, P las the laser output power, L ins the optical insertion losses, η the MZ extinction ratio, V DC the MZ bias and V RF the RF signal.

At the other side of the optical link, the photodiode is described as a quadratic detector using a nonlinear voltage controlled current source, and a low pass filter is added to take into account its frequency response. The optical interference inside the MZ modulator may also be described using an electrical phase modulator available in ADS library [START_REF] Brahimi | CAD of microwave optical systems for time&frequency applications[END_REF]. The main drawback of this technique comes from this circuit element which may only be used with an envelope simulation. The envelope technique is dedicated to the simulation of a slow varying signal superimposed to a fast signal, which is the case of the RF signal compared to the optical signal. However, in terms of noise, we will need the description of the noise conversions between the system three main frequencies: DC, RF and optical (see Figure 4) and the envelope simulator is not able to take into account three different frequency domains. Therefore, only the harmonic balance simulator is used in our simulations, and there are no fundamental differences in terms of computation between the system three main frequencies.

The result of an ADS simulation of the RF output power versus the RF input power for this optical link is depicted in Figure 3. The two studied modulation techniques have been plotted on the same graph: linear modulation (LM) and carrier suppression (DSB-CS). The RF input signal frequency is 10 GHz for the linear modulation and 5 GHz for the carrier suppression case (frequency doubling), and thus the RF output is at 10 GHz. The laser power is 10 dBm, which corresponds to a classical medium power telecommunications laser. These results are close to the ones obtained with analytical models for a similar system [START_REF] Onillon | Optical links for ultra-low phase noise microwave oscillators measurement[END_REF], [START_REF] Guennec | Performance of interferometric systems for optical processing of microwave signals: influence of laser-and microwave-phase noises[END_REF], and [START_REF] Hilt | Microwave harmonic generation in fiber-optical links[END_REF].

However, if compared to measurement, at high level (above 20 dBm) and in the particular case of the LM modulation, some differences appeared between simulation and experiment. These differences may be due to thermal or charge effects at high power in the modulator, which are not described in the model. This discrepancy is still under study, but it occurs in an RF power range which is above the one which is effectively foreseen in our application. One of the systems we would like to simulate with this approach is the optical electric oscillator (OEO), and particularly its phase noise performance. This is quite difficult because it is an autonomous system, in which the oscillation start up has to be managed independently from the optical signal. However, the performance of the OEO can be computed from its open loop phase noise, and we have started these investigations by studying phase noise in open loop RF optical links and systems.

Figure 4 represents the various carriers (either microwave or optical) which are interacting in our systems, and their noise sidebands. These noise sidebands are correlated through the system nonlinear elements, and the choice of ADS for these investigations has been based mainly on the ability of this software to take into account these correlations thanks to a conversion matrices approach in harmonic balance [START_REF] Rizzoli | General noise analysis of nonlinear microwave circuits by the piecewise harmonic-balance technique[END_REF]. The optical carrier is considered in our simulations just like any other carrier, and is described with its noise components: AM noise and FM noise.

The laser model is composed of a frequency source with an associated phase noise spectrum followed by an AM noise modulator. The two noise components are extracted from the measurement.

The laser frequency noise is estimated from the laser linewidth measurement, which is performed using a selfheterodyne measurement bench. At this time, we have made the classical hypothesis of a constant (white) frequency noise for the laser, equal to the laser linewidth divided by π. In a second step, a laser frequency noise measurement set up will allows us to extract the 1/f frequency noise of the laser, which will be included in the model.

The laser relative amplitude noise (RIN) is measured on a dedicated measurement bench, which includes two different set-up: one for the measurement of the laser 1/f RIN, between DC and 100 kHz [START_REF] Onillon | Opticalmicrowave links for LO distribution in space systems[END_REF][START_REF] Brahimi | CAD of microwave optical systems for time&frequency applications[END_REF], and another one for the measurement of the laser microwave RIN, which uses a fast photodiode and a low noise microwave amplifier up to approximately 15 GHz. These data have been used in the noise source associated to the AM modulator of the laser model. Concerning the photodiode, its noise model includes the Schottky white noise, the thermal noise and a 1/f noise component which is difficult to measure but which can be estimated from dual diode receiver measurements. The diode model also includes a nonlinear capacitance, which will be further described.

At this time, the MZ modulator is considered as a nonnoisy (but nonlinear) device.

Figure 5 represents the result of the simulation of the noise component around the DC for the complete MZ based optical link. The simulated noise is divided by the DC carrier, in order to compare it to the laser RIN. One of the interests of this simulation is in determining the phase noise floor, which is related to the carrier to noise ratio at the RF modulation frequency.

Figure 6 depicts the phase noise and amplitude noise simulations around the RF carrier at 10 GHz, obtained with the "pnmx" and "anmx" outputs of ADS software.

Contrary to the result presented in Figure 5, no 1/f phase noise has been computed. Only a 1/f AM noise is visible around the 10 GHz RF carrier. The computed phase noise is thus restricted to the noise/signal ratio, which can be computed from the RIN value and the RF output power at 10 GHz. The absence of 1/f phase noise was unexpected, as 1/f phase noise had previously been measured in such links [START_REF] Onillon | Optical links for ultra-low phase noise microwave oscillators measurement[END_REF][START_REF] Rubiola | Flicker noise in high-speed p-i-n photodiodes[END_REF][START_REF] Bibey | Very low phase-noise optical links-experiments and theory[END_REF]. This noise component is relatively weak (typically weaker than the 1/f phase noise of a microwave amplifier), but it is not negligible. One possible explanation is that we have not included in the model all the 1/f noise sources of the physical system, or not all the nonlinearities. At first, the model included only the laser's 1/f amplitude noise and the nonlinearity of the MZ modulator. This results in a relatively high level of 1/f amplitude noise around the DC output (this is normal, because the optical link is based on amplitude detection), but no 1/f phase noise around the RF carrier was computed. We have then added a noise component associated to the photodiode. Direct conversion of low frequency noise into phase noise in this component is possible, but such a process requires a reactive element in the photodiode model to generate the phase modulation by the baseband 1/f noise. Such a conversion could be performed by the diode nonlinear capacitance.

Following published models of photodiodes [START_REF] Dawidczyk | Investigation of Optical-Microwave Frequency Conversion Processes for PIN Photodiode[END_REF], as well as our own measurements of the biased and illuminated photodiode using an impedance meter [START_REF] Brahimi | CAD of microwave optical systems for time&frequency applications[END_REF], we have added to our model this nonlinear capacitance. The problem is that the diode's capacitance is almost constant in the working zone to be used in photodetection (a reverse bias of -6 V). This explains why adding this nonlinearity to the model, together with a 1/f noise source, has not induced any visible 1/f phase noise contribution on the RF output. This problem is still under study at this time. However, we think that the 1/f phase noise contribution has little chance to be generated by the photodiode, or at least that the phenomenon will not be described by a classical photodiode electrical model.

IV. EXAMPLE OF SYSTEM SIMULATION: THE OPTICAL DELAY LINE MICROWAVE FREQUENCY DISCRIMINATOR.

Up to now, the most complex system we have been able to simulate with our CAD approach is a microwave phase noise measurement bench based on a 4 km optical delay line. This system has been realized in our laboratory and is described in another paper [START_REF] Onillon | Optical links for ultra-low phase noise microwave oscillators measurement[END_REF].

The measurement of the phase noise floor of a delay line discriminator is quite difficult. The classical approach suppresses the delay line, in order to cancel the sensitivity of the system to the source phase noise. This technique is valid for classical microwave frequency discriminators. However, in case of microwave-optical frequency discriminator, some noise processes may occur in the optical delay line itself, and it is thus important to characterize the system including this line.

The only technique in this case is to use an ultra high spectral purity source, such as a sapphire microwave oscillator, to check the ability of the microwave-optical measurement bench to characterize ultra low phase noise sources. Such an oscillator at 4.86 GHz is available in our laboratory. It had been realized with a low phase noise SiGe amplifier and a WGM sapphire resonator (Q L ≈ 60,000) [START_REF] Cibiel | Optimization of an ultra low phase noise Sapphire SiGe -HBT oscillator using nonlinear CAD[END_REF].

The phase noise of this oscillator has been measured close to the carrier using an Agilent E5052 phase noise measurement bench. Then the oscillator has been connected to the microwave optical frequency discriminator and the result is plotted in Fig. 8. As shown, the sapphire oscillator is effectively measured by the discriminator and on a wider range of baseband frequencies, although the first spurious peak of the 4 km delay line is clearly visible on this plot around 53 kHz, and prevents the phase noise measurement in its vicinity. The phase noise floor of this system has also been simulated with the approach described in sections I, II and III. The simulated general behaviour is correct, including the noise peaks due to the drop in sensitivity near 53 kHz and its harmonics. Close to the carrier, the simulated phase noise is quite optimistic due to the absence of 1/f noise.

However, this validates our approach on a complex system, which would be very difficult to model with a classical analytical approach.

V. CONCLUSION Our modelling approach is able to describe the main parameters of a microwave optical link, such as the power gain or the signal to noise ratio. The simulation of the optical link additive phase noise has also been performed, but the result obtained can only be related at this time to the signal to noise ratio. No significant 1/f phase noise has been simulated, and the 1/f component of the spectra around the RF carrier is either related to the amplitude noise. Further investigations are in progress, particularly to use this approach in different systems such as microwave optical oscillators.

Fig. 1

 1 Fig. 1 MZ modulator optical power response versus DC bias voltage, and bias points for RF modulation

Fig. 2

 2 Fig. 2 SDD model of the MZ modulator and photodiode model

Fig. 3

 3 Fig. 3 RF output power versus RF input power of the optical link simulated and measured (10 GHz output frequency) III. MZ MODULATOR BASED OPTICAL LINK MODEL: RF NOISE AND PHASE NOISE.

Fig. 4

 4 Fig. 4 Schematics of the noise conversion processes between the different carrier and their harmonics: DC, RF and optical

Fig. 5 Fig. 6

 56 Fig. 5 ADS simulation of the noise to DC carrier ratio at the output of the optical link

Fig. 7 (

 7 Fig. 7 (a) Scheme of the optical link phase noise measurement bench using the sapphire and (b) Agilent phase noise measurement bench used to evaluate the phase noise of the sapphire oscillator.

  Simulated phase noise of the discriminator (4km delay) Sapphire oscillator measured with the (4km delay) discriminator Sapphire oscillator measured with the E5052B

Fig. 8

 8 Fig. 8 Simulated and measured phase noise of the optical-microwave delay line frequency discriminator (4 km delay line)


L A De

Moyenne Classe

A Superieure

INDE" CEBEILLAC Delhi

Alexandre

Rault Yves-Marie

TWITTER DATA IN THE STUDY OF A SOCIAL GROUP'S ACTIVITY SPACE. THE CASE OF THE UPPER MIDDLE CLASS IN DELHI, INDIA "CONTRIBUTION A L'ETUDE DE L'ESPACE D'ACTIVITE D'UN GROUPE SOCIAL DES DONNEES TWITTER GEO-LOCALISEES. LE CAS

Keywords: Activity space, Twitter, social networking service, social media, geotagged data, luxury shoppers, upper middle class, Delhi, India Espaces d'activité, Twitter, réseaux sociaux, données géo-localisées, consommateurs du luxe, Delhi, Inde

Since 2009, the social media Twitter provides free access to localization data consisting of geotagged messages sent on the platform. We used this data to highlight their potential contributions to the study of social groups' activity space. Using a sample of luxury shoppers, we analyzed the daily activity and mobility patterns of the upper middle class in Delhi, India. We intersected these data with the results of an ethnographic study carried out in two luxury shopping places in Delhi and found that the lower middle class was overrepresented in the Twitter sample. We argue that the varying motivation to post on social media tend to skew the representativeness of social groups sampled on a spatial criterion. We eventually advocate the complementary use of geotagged social media data and qualitative data based on ethnographic research.

INTRODUCTION

The number of single smartphone users in India has increased considerably in the past decade, particularly in urban areas. These devices facilitate the obtaining of data the geographic position of users, which several applications use to provide personalized services. In India, where data on mobility or activity spaces is often difficult to find, the increasing use of smartphones offer new possibilities for research in geography and social sciences; however, this data is often the property of private service providers, and public access to the data is limited. Twitter (since 2009) has been a significant exception, and provides the most comprehensive database of user locations. It thus allows new possibilities for research on activity space, defined in 1971 by Horton and Reynolds as the "the subset of all urban locations with which the individual has direct contact as the result of dayto-day activities" [START_REF] Perkins | Theory and data for simulating fine-scale human movement in an urban environment[END_REF].

While several studies have already used Twitter datasets, very few of them have dealt with spatiotemporal and human daily mobility analysis [START_REF] Steiger | An Advanced Systematic Literature Review on Spatiotemporal Analyses of Twitter Data[END_REF]. Nevertheless, some studies have highlighted the feasibility of using geotagged tweets to observe human mobility patterns at a global scale [START_REF] Hawelka | Geo-located Twitter as the proxy for global mobility patterns[END_REF] at a country scale [START_REF] Jurdak R | Understanding human mobility from Twitter[END_REF][START_REF] Liu | Multi-scale population and mobility estimation with geo-tagged tweets[END_REF], and at a city scale (Cebeillac et al., 2017). However, the socio-spatial picture depicted by these studies does not provide an accurate picture of human mobility. Twitter users are never, at the global scale, or at the country scale, representative of socially diverse populations due to several reasons. First of all, Twitter users are unevenly distributed over space. In 2016, Twitter claimed 316 million active users worldwide, with a penetration rate more than ten time higher in South America than in Africa and in India [START_REF] Hawelka | Geo-located Twitter as the proxy for global mobility patterns[END_REF]. Secondly, they are unevenly distributed over the social spectrum, with notably certain professions and social classes having a more regular use than others [START_REF] Preoţiuc- | An analysis of the user occupational class through Twitter content[END_REF].

To our knowledge, only one study has used geotagged Twitter data to observe a particular social group in its urban setting. However, the sample used was selected on the basis of a common ethnic and racial background estimated through nicknames and messages analysis [START_REF] Luo | Explore spatiotemporal and demographic characteristics of human mobility via Twitter: A case study of Chicago[END_REF].

In this article, we identified a social group, the upper middle class, based on its presence in one of its place of leisure. We explore the possibilities offered by these datasets to study a specific social group's activity space. In India, the use of Twitter is particularly well segmented along socio-economic lines, since Twitter requires a good command of the English language and the ownership of a smartphone with 3G or 4G network. Only a quarter of the population is able to buy consumer goods beyond basic necessities [START_REF] Sridharan | The Growth and Sectoral Composition of India's Middle Classes: Their impact on the politics of economic liberalization[END_REF]. While 350 million persons use the Internet at least once a year, 97 million of them are active social media users on their mobile phones3 , among which only 46 million individuals have a Twitter account (3,7% of the total population), restricted mostly to urban areas.

As a consequence, we assumed that members of the urban Indian upper middle class, being the ablest to use Twitter, would be a relevant social group for our study. In order to find a representative sample of this class and to study their activity space, we chose to focus on the luxury shoppers in Delhi, one of the top Indian metropolitan city by its GDP per capita. We selected the shoppers of two luxury shopping places in South Delhi, located near the most expensive residential complexes of the city; the Khan Market, a high-street, and the DLF Emporio, a shopping mall. These are two of the most expensive retail destinations in India, with a monthly rental of 1 000 rupees per sq. ft. and 1 250 rupees per sq. ft., respectively4 .

Our study was carried out in two stages. Firstly, in early 2015, we conducted on-site observations and surveys as well as off-site interviews with the users, inquiring about their socio-economic characteristics, place of residence, and places of leisure. The study notably revealed that the two luxury places did not only welcome ultra-highnet-worth individuals, but middle-income consumers as well. Simultaneously, we built a database of luxury shoppers' geotagged locations in Delhi based on a group of people who tweeted at least once in one of the two sites selected for the study.

Combining geotagged data and qualitative data, we explored the possibilities of using geotagged Twitter data in researching social groups. Our study also highlights the drawbacks of Twitter data, especially when not used along with ethnographic research. We will develop our argument in three parts. Firstly, we will thoroughly explain the construction of our database. Secondly, we will critically examine the possibilities it provides for the study of activity space and human mobility. Thirdly, we will demonstrate that the various social motivations to tweet create biases in social groups' representativeness, and eventually argue for the complementary use of geotagged social media and ethnographic data.

THE DATABASE: LOCATION, USER, AND DATE OF TWEETS

Twitter is a micro-blogging service on the Internet, where people can send short messages or "tweets". These messages can be private (shared with friends) or public (visible to everyone). Since 2009, it became possible to add the geolocation of the device via "geotagging" of the message, even if this option is blocked by default5 . The Twitter Streaming API6 allows collecting in real-time of a sample of ~1 % of the total feed of public tweets for free [START_REF] Morstatter | Is the Sample Good Enough? Comparing Data from Twitter's Streaming API with Twitter's Firehose[END_REF][START_REF] Wang | Should We Use the Sample? Analyzing Datasets Sampled from Twitter's Stream API[END_REF]. In this sample, around 10% of the tweets are geotagged, giving us information on the spatial location of the user, with an accuracy depending on the device -up to 30 metres for a smartphone outdoor [START_REF] Zandbergen | Positional Accuracy of Assisted GPS Data from High-Sensitivity GPS-enabled Mobile Phones[END_REF], and up to few kilometres for a computer far from the access point of the Internet service provider.

Between 25 June 2014 and 4 December 2015 (524 days), we have been able to collect a total of 13 672 354 geo-located and dated tweets (with a minute accuracy), for 507 482 unique users in India. However, Twitter users are not always "real persons". The company admitted in 2014 that 8.5% of the active users connect through a tierce service application7 . Since the platform includes a large worldwide audience, it is a good platform for promotion, advertisement or geo-marketing, and is actively used by organizations to bring forwards their products, ideas or causes. Most of the time, these organisations hire a community manager or create a "bot" (twitbot) that can animate the social network of the Twitter account owner [START_REF] Ferrara | The rise of social bots[END_REF]. The geotagged tweets inform us on the ID of the user, but not on its characteristics. Consequently, we had to remove the non-human tweets from our database. We based our bot detection algorithm on the speed between two messages sent by a user so that they are slower than a plane speed [START_REF] Hawelka | Geo-located Twitter as the proxy for global mobility patterns[END_REF][START_REF] Jurdak R | Understanding human mobility from Twitter[END_REF]. But sometimes, two tweets can be sent at the same time from different locations, probably when there are network problems. In that case, the speed is infinite. We considered this bug and chose that users with more than 2% of their tweets sent at a speed higher than 600km/h would be defined as bots. We also excluded users with an average speed higher than 70km/h in urban areas, as this speed is rarely reached in locations like Delhi. We removed all the IDs consisting of 12 hexadecimal digits because they can only be MAC addresses (computers), and all the IDs of 15 hexadecimal digits, which belong to beacons, devices used in geo-marketing. Eventually, we removed all the users with a very high tweet frequency, i.e. higher than 20 tweets a day on an average, which would mean around 2000 public tweets per day, as we could only collect 1% of the tweets.

After removing the robots, we also decided not to consider low activity Twitter users, i.e. with less than 15 active days of tweets, assuming that these users would provide enough locations to perform accurate analysis of the activity spaces. The cleaned database included 5 720 169 tweets for 48 637 unique users accross Indiarespectively 41,8% and 9,58% of the original database. Eventually, in order to keep our focus on Delhi, we selected the tweets that were sent within a 30 km radius of Delhi NCR, generating a final database of 967 379 tweets for 13 349 users.

POTENTIALS OF GEOTAGGED TWITTER DATA

Study of influx

The geotagged tweets, including the date and time when the tweets were sent, provide us with accurate information on influx periods of Twitter users in select locations. In our study, this information proved helpful in finding out the preferred times and days individuals chose for visiting luxury shopping places. The Figure 1 shows the number of users in the two commercial complexes per hour of the week. In the Khan Market, we can see a moderate visiting peak around noon on the weekdays and a major peak in the evening. The data seems aligned to our observation that the highstreet is a popular venue for lunch and dinner among professionals and government officials, due to the proximity to their offices. However, the Emporio, bordering two affluent districts in Delhi, does not attract such a clientele. Outside of lunch and dinner hours, the scarce population of users is mostly composed of women often accompanied by friends or relatives, sometimes for a "kitty party", a meeting between housewives over meal or coffee. In both places, Friday evenings and weekends have the largest influx of visitors, mostly families and youngsters. The data broadly confirm what was observed through qualitative research.

Study of activity space

Place, time, and frequency of visits are the three most important attributes of the activity space of an individual, defined as the set of daily places of living, working, and recreation. To locate such places, most studies adopt methodologies involving questionnaires with open or multiple choice questions. However, self-reported responses to such questionnaires often turn out to be inaccurate. For instance, in the case of our initial study including face-to-face interviews, the users were asked about the places where they usually go for shopping in Delhi. The interviewees gave incomplete answers and could only recall a few major places. Usually, they would give a handful of major locations, from the scale of a shop to the scale of a shopping mall, without providing precise information on the frequency of the visits. On the contrary, the Twitter dataset allows to precisely know about the frequency of visits to places whose functions can be identified using OpenStreetMap (OSM), a mapping community project that contributes to the mapping of roads, railways, and all kind of places in the world (www.openstreetmap.org). The OSM database notably helped us to highlight the functions of each user location, which we obtained by aggregating tweets within a spatial radius using the same method as Jurdak et al. ( 2015) a dbscan approach introduced by Ester et al., 1996 (described in Figure 2). We created clusters of spatial points (tweets) that are all located within a certain distance, 50 meters for this study, implying that in every cluster location, all points should be at an inferior or equal distance to 50 meters. Figure 3 shows the percentage of users having a specific number of locations in their activity space (using a log/log plot). Almost the same ratio has from 1 to 7 locations, but it decreases rapidly after 10, suggesting that most users visit few different places, with a little amount of them having tweeted in many different locations. It is noteworthy that most Twitter users have few places in their activity space. Among all the tweets sent in Delhi, 11% were located in an OSM spatial polygon (55% on a major road, 45% in another kind of place). Due to differences in size, function and public of each place, and the absence of several places in the OSM database, we found significant differences in the amount of geotagged tweets in each location. In order to compare the activity spaces of the luxury shoppers with other Twitter users, we created three kinds of datasets: (i) Twitter users that don't visit malls, (ii) Twitter users visiting shopping malls in Delhi (except Khan Market and DLF Emporio) and (iii) Twitter users visiting Khan Market and DLF Emporio. When gathering the clusters maps of Twitter users at different time periods of the day, we can observe the "urban pulsations", showing mobility and activity patterns in Delhi. If we compare the three snapshots of geotagged tweets sent from 7 to 8 pm, we observe that people have different mobility and activity patterns (Figure 4). For instance, while the map with all Twitter users shows that they are wide-spread across the city, they tend to be more narrowly clustered for the shopping mall and luxury shoppers. The latter are less present in East Delhi and Dwarka (middle-income suburbs), while they are more present in South Delhi and Gurgaon, the two most expensive residential areas of Delhi region.

In each Twitter user category, people exhibit different preferences for shopping locations. Drawing on our sample of people who had tweeted at least once in the two luxury commercial places, we were able to identify four shopping places that these users often visit too (see Figure 5, Figure 6), two high-end shopping mall and two high streets. The two high streets (Connaught Place and Hauz Khas village) also include walking spaces, historical monuments, and parks. Consequently, the tweets might not always be sent by consumers but also by visitors and walkers. This bias could be avoided through questionnaires. However, using geotagged Twitter data has the benefit to avoid imposing answers, for instance through the selection of a few places on the assumption that they are the most visited. However, it remains important to look at the configuration of each place to understand discrepancies in results. For instance, the Khan Market is a "high street", a commercial concept consisting of a pedestrian street composed of various shops. On the other hand, the DLF Emporio is a "shopping mall", i.e. a commercial form consisting of one or several buildings forming a complex of shops connected by air-conditioned walkways enabling customers to walk from stores to stores without going outside. While the mall mostly includes apparel and accessories stores with a large number of flagship international brands like Louis Vuitton or Chanel, located on the first floor and advertised on the building's facade, the Khan Market is a multifunctional high-street where we find garment stores, jewelers, book and electronic stores as well as grocery shops and restaurants, with a large price range, even though the products and services are relatively very costly. A study of 6 markets in Delhi undertaken by Sarma in 2005 [START_REF] Sarma | The social logic of shopping: a syntactic approach to the analysis of spatial and positional trends of community centre markets in New Delhi[END_REF]) also showed that locations of the shopping places in the urban grid explain large differences in consumer demographics. The Khan Market, centrally located on important routes of the city, has a high potential for attracting long range consumers from vehicular, bus and metro traffic, as well as several passing local pedestrian traffic due to its good connections to walkways, and the capacity to support vehicular and pedestrian movement on site and provide with a large quantity of parking space. This is not the case for the DLF Emporio which has been configured largely to host a public of car-owners.

Study of places of residence

Amongst all the places in the activity space, those which provide the most valuable information on the social backgrounds are probably the places of residence. We explained earlier how we were able to define clustered locations for each user. In order to identify the residential places, we created an algorithm to find out which one of them were homes of the Twitter users. Firstly, candidate locations could not be in places considered by OSM as leisure places, malls, park, or road. Consequently, we removed all those places. Then, we adapted the method used by [START_REF] Ahas R | Daily rhythms of suburban commuters' movements in the Tallinn metropolitan area: Case study with mobile positioning data[END_REF][START_REF] Calabrese | AllAboard: A System for Exploring Urban Mobility and Optimizing Public Transport Using Cellphone Data[END_REF], defining home locations as the cluster where the users were active during the most different days, and especially during the night hours -9 pm to 7 am (Cebeillac et al, 2017). Since the Twitter database is not representative of all Delhi inhabitants, this algorithm just provide an estimation of home locations of Twitter users. However, we were able to detect the home of 6324 users in Delhi for 881333 tweets in 130308 locations.

If we look at the entire Twitter dataset, we can observe four main poles, namely Gurgaon, South Delhi, East Delhi and West Delhi, with higher densities in South and East Delhi (Figure 7), with reducing density in the shopping mall dataset (Figure 7). As for the luxury shoppers dataset (Figure 7) accounting for only 164 users who tweeted in the Khan Market or in the DLF Emporio, it is noteworthy that two poles appear more clearly in South Delhi and Gurgaon, the most expensive areas of the city. On the contrary, the middle-income areas of West and East Delhi (Noida excepted) are not on the map anymore. In order to estimate the social class of individuals of our two samples, we've linked the home locations (declared during the survey and estimated for Twitter users) with the property tax level, ranging from H (minimum) to A maximum) for 2106 colonies in Delhi in 2010 (Figure 8). We assume that the property tax is a good proxy and provide valuable information on the socioeconomic categories of the users, even if it is worth noting that urban villages like Hauz Khas village tend to have a very low tax level even though they host significant numbers of high-income households. Indeed, in wealthy neighbourhoods, active neighbour welfare associations tend to militate to downgrade the rate of their property tax [START_REF] Telle | Aedes : Analyse de l'émergence de la dengue et simulation spatiale[END_REF].

Finally, 131 home locations from the survey were defined at the colony wise level. It is relatively small due to the inaccuracy of the locations given by the interviewees. On the other hand, 164 home location were estimated for the Twitter users that visit Khan Market and Emporio.

In order to compare the two dataset with Delhi global population, we've estimated the population per colony (as the population is only available ward wise). To do so, we've detect built-up areas (using Kmeans algorithm on Landsat-8 images) and merged them with the 2011 ward-wise census, assuming a homogeneous population per ward. We've created a grid of 250m cells with the population estimation that we've intersected with the colony shapefile.

Figure 9 allow to compare the percentage of population from the survey and from the census that lives in a colony with a specific property tax category. It shows that less of 10% of the Delhiites live in wealthy colonies (A or B), this percentage rise to more 80% for our survey sample, confirming that customers of Khan market and Emporio lives in the most expensive areas of the city. While 70% of Delhi inhabitants stays in quite low property tax colonies (from D to H), it concern only few interviewees, and they lives in wealthy urban villages. If we compare the results of the survey to the Twitter database (Figure 10), we can notice that sample of Twitter users is more wide-spread among the different property tax categories. It thus clearly appears that there is an under-representation of high-income users in the Twitter database compared to the interviewees (Figure 10). Nevertheless, in both cases, luxury shoppers are over-represented in high-income areas as compared to the actual population who live there. The discrepancies between the survey and Twitter datasets indicate that people who tweet in luxury shopping places are not as wealthy as most of the typical luxury shoppers. In the last part of this article, we will try to understand why members of the lower middle class tend to tweet and geotag their tweets more than other groups in luxury shopping places, thus highlighting the limitations of using Twitter data to identify a social group based on its presence in a specific place.

TWITTER IN CONTEXT: WHO REALLY TWEETS IN LUXURY SHOPPING PLACES?

To our knowledge, there has been no sociological research on Twitter users in India, despite one study on the use of social media in South India [START_REF] Miller | How the world changed social media[END_REF] making it difficult to integrate potential biases in the dataset based on age, gender or social categories of the users. We do not have much information on why Indian Twitter users generally post messages. However, studies in other countries have shown that Twitter is mainly used by the younger generations, both as a platform to express opinions and as a social network. The first use likely reduces the number of geotagged tweets people send, since it mostly consists of sharing personal thoughts, general information, or media content. In the other case, when users geotag the tweets they send, we can assume that they are using it as a social network since such information could be only of interest to interpersonal relation circles (Figure 11). Twitter users often share a photo through Facebook or Instagram. In that case, tweeting becomes a way to put forward a meliorative personal information with their followers (Figure 12).

Drawing on the concept of conspicuous consumption8 , we can further assume that people tweet in luxury places in order to gain prestige, esteem and sense of importance. Indeed, luxury consumption in India, like in many places globally, particularly in developing countries, is a marker of success. Moreover, shopping malls and international brands are major symbols of modernity, giving consumers a sense of "world-class" belonging and a taste of what is perceived as "first-class" or "five-star" lifestyles [START_REF] Brosius | India's middle class: new forms of urban leisure, consumption and prosperity[END_REF]. When surveyed, several consumers of the DLF Emporio complained about the noisiness and bad crowd of traditional Indian shopping places and reported that they preferred comfortable environments like shopping malls rather than open markets, which reminded them of the Indian "bazaars", which convey archaic imaginaries. Among the luxury shoppers, we would thus find a considerable number of individuals with limited purchasing power, coming to experience new luxurious and so-called modern environments. In India, consumption has indeed become a marker of middle-class belongingness in the last two decades [START_REF] Varma | The new Indian middle class: the challenge of 2014 and beyond[END_REF][START_REF] Cadene | Classes moyennes et construction d'une modernité indienne. Le cas des « shopping malls » à Delhi[END_REF]. This is notably illustrated by the slogan of the DLF Emporio, "experience luxury". Consequently, the users are not necessarily consumers. For instance, in a study on shopping malls in India, sociologist Nita Mathur, showed that among the people who visited the mall regularly, only 20%, the "serious buyers", had disposable income at hand, while the remaining 80% consisting of "casual buyers", mainly youngsters, came to familiarize themselves with the latest fashion trends or spend time with friends [START_REF] Mathur | Shopping Malls, Credit Cards and Global Brands: Consumer Culture and Lifestyle of India's New Middle Class[END_REF]. Accounts of shop sellers in the luxury shopping places, reporting the lack of customers in their stores, confirmed that many of the visitors did not make any purchases. We could also observe that many users did not feel comfortable enough to enter the shops and would remain in the alleys, observing products through the window, limiting themselves to buying a beverage in the cafés. The low consumption levels actually have consequences on the profitability of international luxury brands. Several of them had to leave India prematurely or are still struggling to become profitable and convince price conscious Indian customers 9 . For instance, Bottega Veneta, an Italian house specialized in leather goods, had to downsize its store area by half and move it in an older section of the DLF Emporio mall. With the resistance of small retailers, the difficulties to adjust to the diversity of the Indian consumer, the lack of commercial infrastructures and an adverse legislation, retailing multinationals are facing considerable hardships to penetrate the Indian market (Rault 2015). Actually, with only 2% share of the global luxury market, India trails well behind other emerging nations, China in particular (30%). From the Indian ultra-high-net-worth individuals (127 000)10 to those who own both a TV, a computer, a vehicle (two or four wheeler) and a phone (only 4,6% of total households), there seem to be relatively fewer typical luxury consumers in India11 . Actually, the old elite has mostly continued to buy luxury goods abroad due to limited availability of products and late arrival of new collections.

As a result, luxury shopping places are home to different social strata, also because, as Veblen wrote, middle class members imitate the consumption practices of the upper class in order to improve their social status [START_REF] Veblen | The theory of the leisure class, Dover thrift editions[END_REF]. On the contrary, regular customers and serious buyers do not feel the need to display activities of luxury shopping because it is a habit. They do not build their social status by showing their capacity to consume but by their ways of consuming, as it was highlighted in the monumental work by Pierre Bourdieu, La Distinction [START_REF] Bourdieu | La Distinction. Critique sociale du jugement[END_REF]. In doing so, they distinguish themselves from the lower groups. Several users who considered themselves as regular and serious customers thus look down upon people who wear loud colors and logos, show off brands, take selfies 12 and use social networks to display their habits. This is the case of Arjun, a 30 years old architect and a regular customer at DLF Emporio. According to their experience, social background, caste, class, origin or income, individuals do not have the same ways of tweeting, and in India, society is highly fragmented on those many lines [START_REF] Deshpande | Contemporary India: a sociological view[END_REF]. In the case of the users of luxury shopping places, people who are not familiar with luxury environments might be more prone to tweet there than regular customers. Consequently, the assumption that luxury shoppers would tweet equally seems to be wrong, partly explaining why middle-income groups are over-represented in the Twitter sample. We can thus conclude that the Twitter users in luxury shopping places are not representative of the Indian middle upper class.

CONCLUSION

To conclude, we can affirm that the use of social media geotagged data provides us with new perspectives on social groups' activity space and mobility. However, if selected on the basis of the sending of a message from a place, the sample might not be representative of the social group the study initially intended to follow, due to the various social incentives to post on social media and the varying social backgrounds of the individuals.

Consequently, there is a need for a mix use of Twitter data and ethnographic methods. First of all, Twitter data can be a major help to the ethnographer, since it facilitates the inclusion of a large variety of locations in a study. This way, there are more possibilities for comparative approaches at various scales. When merged with other spatial information data (such as OpenStreetMap or Google place), such data can also help in a great way in analyzing social groups' activity space and mobility, as well as lifestyles. For instance, luxury shopping places could seem to be an accessible and easygoing place of study, but it is not. Customers seldom want to spend time answering questions during their leisure moments; their answers are often inaccurate and partial; it consequently takes a lot of time and resources to collect a significant sample of customers; and finally, official authorizations for studies in private places are often difficult to obtain. With Twitter data, the researcher does not need the agreement of the users to inquire about their practices. Even though the Twitter users supposedly know that the information they give out is public since they signed the user agreement, they do not know that this data could serve in tracking their movements, even for scientific purposes. This is an ethical question which remains unsolved in this paper, but would deserve a larger discussion.

Eventually, and we would like to stress it, there is a need to do ethnographic research in order to accurately use social media data. Integrating the social representations of the users can help in identifying potential limitations in geotagged data, and perhaps, being aware, integrate the potential biases in the analysis.

Figure 1 :

 1 Figure 1: Visiting frequency of Twitter users in two luxury shopping places.

Figure 2 :

 2 Figure2: A theoretical activity space of a user, where each location is aggregated into a cluster using the dbscan method. In this case, 20 locations are merged in 4 clusters (or activity centers).

Figure 3 :

 3 Figure 3: Number of locations in the activity space per user (log/log).

Figure 4 :

 4 Figure 4: Twitter users density between 7 and 8pm. From left to right: users who never visit shopping malls, users who visit shopping malls (Khan Market and Emporio excluded); users who visit Khan Market and/or DLF Emporio. Sources: Twitter dataset; Made with R using ggplot2 and ggmap.

Figure 5 :

 5 Figure 5: Visiting frequency of luxury shoppers in the two top shopping malls in terms of total frequentation.

Figure 6 :

 6 Figure 6: Visiting frequency of luxury shoppers in the two top high streets in terms of total frequentation.

Figure 7 :

 7 Figure 7: Home density of Twitter users. From left to right: Twitter users who never visit malls; Twitter users who visit malls (Khan Market and Emporio excluded); Twitter users who visit Khan Market and/or Emporio.Sources: Twitter dataset. Made with R using ggplot2.

Figure 8 :

 8 Figure 8: Map with property tax categories and location of shopping malls in Delhi. Sources: www.mcdpropertytax.in, provided by O. Telle et B. Lefevbre. Made with qgis.

Figure 9 :

 9 Figure 9: Percentage of Delhi inhabitants and persons from the survey in each property tax category. From a dasymetric map of the census 2011.

Figure 10 :

 10 Figure 10: Percentage of Twitter and surveyed luxury shoppers in each property tax category.

Figure 11 :

 11 Figure 11: Two geotagged tweets sent from the DLF Emporio.

Figure 12 :

 12 Figure 12: 4 photos posted on Twitter via Instagram (above) and 2 photos posted directly on Twitter (below) from the DLF Emporio.

"

  If I open my Facebook right now there will plenty of friends posting selfies with friends in Emporio. Digital world has made people stupid, imbecile. It is about keeping displaying their habits and everything. It is about being loud in the open. If you see my activity on Facebook, I don't post anything on my page. It is a social service supposed to connect people, not to display your entire habits."

University of Rouen, alexandre.cebeillac@etu-univ-rouen.fr

Paris Diderot University, yves.marie.rault@gmail.com

Digital, Social & Mobile in India in 2015, WeAreSocial, 2015, http://wearesocial.sg/?s=india, consulted on 15.07.2016.

Cushman & Wakefield, New Retail Frontiers: Emerging Main Streets in India, 2014.

Twitter Terms of Service (https://twitter.com/tos?lang=en).

https://dev.Twitter.com/streaming/overview, consulted on 02.05.2016.

https://www.sec.gov/Archives/edgar/data/1418091/000156459014003474/twtr-10q_20140630.htm, consulted on 03.05.2016.

The concept was coined by the sociologist and economist Thorstein Veblen in his seminal work « Theory of the Leisure Class », in 1899. He defines « conspicuous consumption » as the act of spending on unnecessary items in a way that makes people notice it in order to display or attempt to increase one's social status.

"Luxury retailers shrink outlets to maximise profits", 09.04.2012, The Economic Times, http://articles.economictimes.indiatimes.com/2012-04-09/news/31313147_1_luxury-brandsabhay-gupta-retail-space.

Top of the Pyramid 2015. Decoding the Ultra HNI., Kotak, 2015.

Government of India, "Census of India", 2011.

ACKNOWLEDGMENT

The authors would like to thank the organizers of the 18th AJEI (Association des Jeunes Etudes Indiennes) workshop for providing a stimulating forum to present and discuss their results.